Computer-generated holography technology has been widely applied,and as research in this field deepens,the demand for memory and computational power in small AR and VR devices continues to increase.This paper presents...Computer-generated holography technology has been widely applied,and as research in this field deepens,the demand for memory and computational power in small AR and VR devices continues to increase.This paper presents a hologram generation method,i.e.,a symmetrically high-compressed look-up table method,which can reduce memory usage by50%.In offline computing,half of the basic horizontal and vertical modulation factors are stored,halving the memory requirements without affecting inline speed.Currently,its potential extends to various holographic applications,including the production of optical diffraction elements.展开更多
Obtaining the vertical distribution profile of trace gas is of great significance for studying the diffusion procedure of air pollution.In this article,a look-up table method based on multi-axis differential optical a...Obtaining the vertical distribution profile of trace gas is of great significance for studying the diffusion procedure of air pollution.In this article,a look-up table method based on multi-axis differential optical absorption spectroscopy(MAX-DOAS)technology is established for retrieving the tropospheric NO_(2) vertical distribution profiles.This method retrieves the aerosol extinction profiles with minimum cost function.Then,the aerosol extinction profiles and the atmospheric radiation transfer model(RTM)are employed to establish the look-up table for retrieving the NO_(2) vertical column densities(VCDs)and profiles.The measured NO_(2) differential slant column densities(DSCDs)are compared with the NO_(2) DSCDs simulated by the atmospheric RTM,and the NO_(2) VCDs,the weight factor of NO_(2) in the boundary layer,and the boundary layer height are obtained by the minimization process.The look-up table is established to retrieve NO_(2) VCDs based on MAX-DOAS measurements in Huaibei area,and the results are compared with the data from Copernicus Atmospheric Monitoring Service(CAMS)model.It is found that there are nearly consistent and the correlation coefficient R2 is more than 0.86.The results show that this technology provides a more convenient and accurate retrieval method for the stereoscopic monitoring of atmospheric environment.展开更多
The current exact Rayleigh scattering calculation of ocean color remote sensing uses the look-up table (LUT), which is usually created for a special remote sensor and cannot be applied to other sensors. For practica...The current exact Rayleigh scattering calculation of ocean color remote sensing uses the look-up table (LUT), which is usually created for a special remote sensor and cannot be applied to other sensors. For practical application, a general purpose Rayleigh scattering LUT which can be applied to all ocean color remote sensors is generated. An adding-doubling method to solve the vector radiative transfer equation in the plane-parallel atmosphere is deduced in detail. Compared with the exact Rayleigh scattering radiance derived from the MODIS exact Rayleigh scattering LUT, it is proved that the relative error of Rayleigh scattering calculation with the adding-doubling method is less than 0.25%, which meets the required accuracy of the atmospheric correction of ocean color remote sensing. Therefore, the adding-doubling method can be used to generate the exact Rayleigh scattering LUT for the ocean color remote sensors. Finally, the general purpose exact Rayleigh scattering LUT is generated using the adding-doubling method. On the basis of the general purpose LUT, the calculated Rayleigh scattering radiance is tested by comparing with the LUTs ofMODIS, SeaWiFS and the other ocean color sensors, showing that the relative errors are all less than 0.5%, and this general purpose LUT can be applied to all ocean color remote sensors.展开更多
The BeiDou software receiver uses the fast Fourier transform(FFT)to perform the acquisition.The Doppler shift estimation accuracy should be less than 500 Hz to ensure satellite signals to enter a locked state in the t...The BeiDou software receiver uses the fast Fourier transform(FFT)to perform the acquisition.The Doppler shift estimation accuracy should be less than 500 Hz to ensure satellite signals to enter a locked state in the tracking loop.Since the frequency step is usually 500 Hz or larger,the Doppler shift estimation accuracy cannot guarantee that satellite signals are brought into a stable tracking state.The straightforward solutions consist in increasing the sampling time and using zero-padding to improve the frequency resolution of the FFT.However,these solutions intensify the complexity and amount of computation.The contradiction between the acquisition accuracy and the computational load leads us to research for a more simple and effective algorithm,which achieves fine acquisition by a look-up table.After coarse acquisition using the parallel frequency acquisition(PFA)algorithm,the proposed algorithm optimizes the Doppler shift estimation through the look-up table method based on the FFT results to improve the acquisition accuracy of the Doppler shift with a minimal additional computing load.When the Doppler shift is within the queryable range of the table,the proposed algorithm can improve the Doppler shift estimation accuracy to 50 Hz for the BeiDou B1I signal.展开更多
Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (...Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.展开更多
To quantify the seismic effectiveness of the most commonly used fishing line tie up method for securing museum collections and optimize fixed strategies for exhibitions,shaking table tests of the seismic systems used ...To quantify the seismic effectiveness of the most commonly used fishing line tie up method for securing museum collections and optimize fixed strategies for exhibitions,shaking table tests of the seismic systems used for typical museum collection replicas have been carried out.The influence of body shape and fixed measure parameters on the seismic responses of replicas and the interaction behavior between replicas and fixed measures have been explored.Based on the results,seismic effectiveness evaluation indexes of the tie up method are proposed.Reasonable suggestions for fixed strategies are given,which provide a basis for the exhibition of delicate museum collections considering the principle of minimizing seismic responses and intervention.The analysis results show that a larger ratio of height of mass center to bottom diameter led to more intense rocking responses.Increasing the initial pretension of fishing lines was conducive to reducing the seismic responses and stress variation of the lines.Through comprehensive consideration of the interaction forces and effective securement,it is recommended to apply 20%of breaking stress as the initial pretension.For specific museum collections that cannot be effectively protected by the independent tie up method,an optimized strategy of a combination of fishing lines and fasteners is recommended.展开更多
To solve the hardware deployment problem caused by the vast demanding computational complexity of convolutional layers and limited hardware resources for the hardware network inference,a look-up table(LUT)-based convo...To solve the hardware deployment problem caused by the vast demanding computational complexity of convolutional layers and limited hardware resources for the hardware network inference,a look-up table(LUT)-based convolution architecture built on a field-programmable gate array using integer multipliers and addition trees is used.With the help of the Winograd algorithm,the optimization of convolution and multiplication is realized to reduce the computational complexity.The LUT-based operator is further optimized to construct a processing unit(PE).Simultaneously optimized storage streams improve memory access efficiency and solve bandwidth constraints.The data toggle rate is reduced to optimize power consumption.The experimental results show that the use of the Winograd algorithm to build basic processing units can significantly reduce the number of multipliers and achieve hardware deployment acceleration,while the time-division multiplexing of processing units improves resource utilization.Under this experimental condition,compared with the traditional convolution method,the architecture optimizes computing resources by 2.25 times and improves the peak throughput by 19.3 times.The LUT-based Winograd accelerator can effectively solve the deployment problem caused by limited hardware resources.展开更多
The previous methods of figuring the numbers of chemical elements is summed up in this paper. Based on that, another two creative calculative methods are introduced as well.
The spatial prediction of the water table can be used for many applications related to civil works (foundations, excavations) and other urban and environmental management activities. Deterministic and geostatistical i...The spatial prediction of the water table can be used for many applications related to civil works (foundations, excavations) and other urban and environmental management activities. Deterministic and geostatistical interpolation methods were used to predict the spatial distribution of water table levels (unconfined aquifers) of important geological formations of the Joao Pessoa City (capital of Paraiba State, Brazil) with dense urban occupation and high demand for new civil works. The deterministic (topo to raster) and geostatistical (ordinary kriging) interpolation methods were evaluated using a Geographic Information System (GIS)-based investigation. The water table levels were obtained from 276 boring logs of Standard Penetration Test (SPT) in situ investigation distributed over the geological formations studied (an area of 59.8 km<sup>2</sup>, covering 40 districts of the Joao Pessoa City). The Nspt values and textural characterization data are stored for levels of 1 m depth. Some boreholes located in the area investigated were not included in the interpolation processes in order to be compared with estimated values (validation of the results). Maps of the water table depths were also produced to further analyze the quality of the water table surfaces interpolated by both methods. The phreatic surface interpolations provided satisfactory results for both methods (RMSE = 1.8 m). The topo to raster method showed a slight general tendency to be less affected by local values in relation to the kriging method and also has the advantage of integrating the drainage flow system, which is a relevant aspect for spatial models of the water table levels of unconfined aquifers. The ordinary kriging (geostatistical method) provides a prediction surface and some measure of the certainty or accuracy of the predictions.展开更多
Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic per...Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic performance is still quite limited and seismic design procedures are not included in current design codes. This paper describes a series of shaking table tests the authors performed on a scaled utility tunnel model to explore its performance under earthquake excitation. Details of the experimental setup are first presented focusing on aspects such as the design of the soil container, scaled structural model, sensor array arrangement and test procedure. The main observations from the test program, including structural response, soil response, soil-structure interaction and earth pressure, are summarized and discussed. Further, a finite element model (FEM) of the test utility tunnel is established where the nonlinear soil properties are modeled by the Drucker- Prager constitutive model; the master-slave surface mechanism is employed to simulate the soil-structure dynamic interaction; and the confining effect of the laminar shear box to soil is considered by proper boundary modeling. The results from the numerical model are compared with experiment measurements in terms of displacement, acceleration and amplification factor of the structural model and the soil. The comparison shows that the numerical results match the experimental measurements quite well. The validated numerical model can be adopted for further analysis.展开更多
A shake-table experiment on pile foundations in liquefi able soils composed of liquefi able sand and overlying soft clay is studied. A three-dimensional(3D) effective stress fi nite element(FE) analysis is employed to...A shake-table experiment on pile foundations in liquefi able soils composed of liquefi able sand and overlying soft clay is studied. A three-dimensional(3D) effective stress fi nite element(FE) analysis is employed to simulate the experiment. A recently developed multi-surface elasto-plastic constitutive model and a fully coupled dynamic inelastic FE formulation(u-p) are used to model the liquefaction behavior of the sand. The soil domains are discretized using a solid-fl uid fully coupled(u-p) 20-8 noded brick element. The pile is simulated using beam-column elements. Upon careful calibration, very good agreement is obtained between the computed and the measured dynamic behavior of the ground and the pile. A parametric analysis is also conducted on the model to investigate the effect of pile-pinning, pile diameter, pile stiffness, ground inclination angle, superstructure mass and pile head restraints on the ground improvement. It is found that the pile foundation has a noticeable pinning effect that reduces the lateral soil displacement. It is observed that a larger pile diameter and fi xed pile head restraints contribute to decreasing the lateral pile deformation; however, a higher ground inclination angle tends to increase the lateral pile head displacements and pile stiffness, and superstructure mass seems to effectively infl uence the lateral pile displacements.展开更多
An interval Pade-type approximation is introduced and then Routh-Pade-type method (IRPTM) is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table...An interval Pade-type approximation is introduced and then Routh-Pade-type method (IRPTM) is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No.62205350)the Special Project of Central Government Guiding Local Science and Technology Development in Beijing 2020 (Grant No.Z20111000430000)the Guangxi Nanning Key R&D Program (Grant No.20233067)。
文摘Computer-generated holography technology has been widely applied,and as research in this field deepens,the demand for memory and computational power in small AR and VR devices continues to increase.This paper presents a hologram generation method,i.e.,a symmetrically high-compressed look-up table method,which can reduce memory usage by50%.In offline computing,half of the basic horizontal and vertical modulation factors are stored,halving the memory requirements without affecting inline speed.Currently,its potential extends to various holographic applications,including the production of optical diffraction elements.
基金the National Natural Science Foundation of China(Grant No.41875040)the Top-notch Talents Program in Universities of Anhui Province,China(Grant No.gxbjZD2020067)the Natural Science Research Projects of Universities in Anhui Province,China(Grant No.KJ2020A0029).
文摘Obtaining the vertical distribution profile of trace gas is of great significance for studying the diffusion procedure of air pollution.In this article,a look-up table method based on multi-axis differential optical absorption spectroscopy(MAX-DOAS)technology is established for retrieving the tropospheric NO_(2) vertical distribution profiles.This method retrieves the aerosol extinction profiles with minimum cost function.Then,the aerosol extinction profiles and the atmospheric radiation transfer model(RTM)are employed to establish the look-up table for retrieving the NO_(2) vertical column densities(VCDs)and profiles.The measured NO_(2) differential slant column densities(DSCDs)are compared with the NO_(2) DSCDs simulated by the atmospheric RTM,and the NO_(2) VCDs,the weight factor of NO_(2) in the boundary layer,and the boundary layer height are obtained by the minimization process.The look-up table is established to retrieve NO_(2) VCDs based on MAX-DOAS measurements in Huaibei area,and the results are compared with the data from Copernicus Atmospheric Monitoring Service(CAMS)model.It is found that there are nearly consistent and the correlation coefficient R2 is more than 0.86.The results show that this technology provides a more convenient and accurate retrieval method for the stereoscopic monitoring of atmospheric environment.
基金supported by the National Natural Science Foundation of China under contract No.40506036the High Tech Research and Development"863"Program of China under contract No.2003AA131160-04the Science and Technology Plan of Zhejiang Province of China under contract Nos 2004E60054 and 2004C13027.
文摘The current exact Rayleigh scattering calculation of ocean color remote sensing uses the look-up table (LUT), which is usually created for a special remote sensor and cannot be applied to other sensors. For practical application, a general purpose Rayleigh scattering LUT which can be applied to all ocean color remote sensors is generated. An adding-doubling method to solve the vector radiative transfer equation in the plane-parallel atmosphere is deduced in detail. Compared with the exact Rayleigh scattering radiance derived from the MODIS exact Rayleigh scattering LUT, it is proved that the relative error of Rayleigh scattering calculation with the adding-doubling method is less than 0.25%, which meets the required accuracy of the atmospheric correction of ocean color remote sensing. Therefore, the adding-doubling method can be used to generate the exact Rayleigh scattering LUT for the ocean color remote sensors. Finally, the general purpose exact Rayleigh scattering LUT is generated using the adding-doubling method. On the basis of the general purpose LUT, the calculated Rayleigh scattering radiance is tested by comparing with the LUTs ofMODIS, SeaWiFS and the other ocean color sensors, showing that the relative errors are all less than 0.5%, and this general purpose LUT can be applied to all ocean color remote sensors.
基金the Open Project of State Key Laboratory of Automotive Simulation and Control,Jilin University(20161108)the National Natural Science Foundation of China(51505221)the Fundamental Research Funds for the Central Universities(NS2019022).
文摘The BeiDou software receiver uses the fast Fourier transform(FFT)to perform the acquisition.The Doppler shift estimation accuracy should be less than 500 Hz to ensure satellite signals to enter a locked state in the tracking loop.Since the frequency step is usually 500 Hz or larger,the Doppler shift estimation accuracy cannot guarantee that satellite signals are brought into a stable tracking state.The straightforward solutions consist in increasing the sampling time and using zero-padding to improve the frequency resolution of the FFT.However,these solutions intensify the complexity and amount of computation.The contradiction between the acquisition accuracy and the computational load leads us to research for a more simple and effective algorithm,which achieves fine acquisition by a look-up table.After coarse acquisition using the parallel frequency acquisition(PFA)algorithm,the proposed algorithm optimizes the Doppler shift estimation through the look-up table method based on the FFT results to improve the acquisition accuracy of the Doppler shift with a minimal additional computing load.When the Doppler shift is within the queryable range of the table,the proposed algorithm can improve the Doppler shift estimation accuracy to 50 Hz for the BeiDou B1I signal.
基金financially supported by the National Natural Science Foundation of China(11202081,11272124,and 11472109)the State Key Lab of Subtropical Building Science,South China University of Technology(2014ZC17)
文摘Global look-up table strategy proposed recently has been proven to be an efficient method to accelerate the interpolation, which is the most time-consuming part in the iterative sub-pixel digital image correlation (DIC) algorithms. In this paper, a global look-up table strategy with cubic B-spline interpolation is developed for the DIC method based on the inverse compositional Gauss-Newton (IC-GN) algorithm. The performance of this strategy, including accuracy, precision, and computation efficiency, is evaluated through a theoretical and experimental study, using the one with widely employed bicubic interpolation as a benchmark. The global look-up table strategy with cubic B-spline interpolation improves significantly the accuracy of the IC-GN algorithm-based DIC method compared with the one using the bicubic interpolation, at a trivial price of computation efficiency.
基金Beijing Nova Program under Grant No.2022036National Key Research and Development Program under Grant No.2019YFC1521000。
文摘To quantify the seismic effectiveness of the most commonly used fishing line tie up method for securing museum collections and optimize fixed strategies for exhibitions,shaking table tests of the seismic systems used for typical museum collection replicas have been carried out.The influence of body shape and fixed measure parameters on the seismic responses of replicas and the interaction behavior between replicas and fixed measures have been explored.Based on the results,seismic effectiveness evaluation indexes of the tie up method are proposed.Reasonable suggestions for fixed strategies are given,which provide a basis for the exhibition of delicate museum collections considering the principle of minimizing seismic responses and intervention.The analysis results show that a larger ratio of height of mass center to bottom diameter led to more intense rocking responses.Increasing the initial pretension of fishing lines was conducive to reducing the seismic responses and stress variation of the lines.Through comprehensive consideration of the interaction forces and effective securement,it is recommended to apply 20%of breaking stress as the initial pretension.For specific museum collections that cannot be effectively protected by the independent tie up method,an optimized strategy of a combination of fishing lines and fasteners is recommended.
基金The Academic Colleges and Universities Innovation Program 2.0(No.BP0719013)。
文摘To solve the hardware deployment problem caused by the vast demanding computational complexity of convolutional layers and limited hardware resources for the hardware network inference,a look-up table(LUT)-based convolution architecture built on a field-programmable gate array using integer multipliers and addition trees is used.With the help of the Winograd algorithm,the optimization of convolution and multiplication is realized to reduce the computational complexity.The LUT-based operator is further optimized to construct a processing unit(PE).Simultaneously optimized storage streams improve memory access efficiency and solve bandwidth constraints.The data toggle rate is reduced to optimize power consumption.The experimental results show that the use of the Winograd algorithm to build basic processing units can significantly reduce the number of multipliers and achieve hardware deployment acceleration,while the time-division multiplexing of processing units improves resource utilization.Under this experimental condition,compared with the traditional convolution method,the architecture optimizes computing resources by 2.25 times and improves the peak throughput by 19.3 times.The LUT-based Winograd accelerator can effectively solve the deployment problem caused by limited hardware resources.
基金This work is supported by the National Science Foundation of China (No. 20471001 and 20671001), the Important Project of Anhui Provincial Education Department (No. ZD2007004-1), the Specific Project for Talents of Science and Technology of Universities of Anhui Province (No. 2005hbz03) and the Key Laboratory of Environment-friendly Polymer Materials of Anhui Province.
文摘The previous methods of figuring the numbers of chemical elements is summed up in this paper. Based on that, another two creative calculative methods are introduced as well.
文摘The spatial prediction of the water table can be used for many applications related to civil works (foundations, excavations) and other urban and environmental management activities. Deterministic and geostatistical interpolation methods were used to predict the spatial distribution of water table levels (unconfined aquifers) of important geological formations of the Joao Pessoa City (capital of Paraiba State, Brazil) with dense urban occupation and high demand for new civil works. The deterministic (topo to raster) and geostatistical (ordinary kriging) interpolation methods were evaluated using a Geographic Information System (GIS)-based investigation. The water table levels were obtained from 276 boring logs of Standard Penetration Test (SPT) in situ investigation distributed over the geological formations studied (an area of 59.8 km<sup>2</sup>, covering 40 districts of the Joao Pessoa City). The Nspt values and textural characterization data are stored for levels of 1 m depth. Some boreholes located in the area investigated were not included in the interpolation processes in order to be compared with estimated values (validation of the results). Maps of the water table depths were also produced to further analyze the quality of the water table surfaces interpolated by both methods. The phreatic surface interpolations provided satisfactory results for both methods (RMSE = 1.8 m). The topo to raster method showed a slight general tendency to be less affected by local values in relation to the kriging method and also has the advantage of integrating the drainage flow system, which is a relevant aspect for spatial models of the water table levels of unconfined aquifers. The ordinary kriging (geostatistical method) provides a prediction surface and some measure of the certainty or accuracy of the predictions.
基金Key Project in the National Science & Technology Pillar Program Under Grant No. 2006BAJ03B03Research Fund for Young Teacher Supported by State Key Laboratory for Disaster Reduction in Civil Engineering Under Grant No. SLDRCE08-C-03
文摘Underground utility tunnels are widely used in urban areas throughout the world for lifeline networks due to their easy maintenance and environmental protection capabilities. However, knowledge about their seismic performance is still quite limited and seismic design procedures are not included in current design codes. This paper describes a series of shaking table tests the authors performed on a scaled utility tunnel model to explore its performance under earthquake excitation. Details of the experimental setup are first presented focusing on aspects such as the design of the soil container, scaled structural model, sensor array arrangement and test procedure. The main observations from the test program, including structural response, soil response, soil-structure interaction and earth pressure, are summarized and discussed. Further, a finite element model (FEM) of the test utility tunnel is established where the nonlinear soil properties are modeled by the Drucker- Prager constitutive model; the master-slave surface mechanism is employed to simulate the soil-structure dynamic interaction; and the confining effect of the laminar shear box to soil is considered by proper boundary modeling. The results from the numerical model are compared with experiment measurements in terms of displacement, acceleration and amplification factor of the structural model and the soil. The comparison shows that the numerical results match the experimental measurements quite well. The validated numerical model can be adopted for further analysis.
基金Major Research Plan of National Natural Science Foundation of China under Grant No.90815009the National Natural Science Foundation of China under Grant Nos.51108134,50378031 and 50178027
文摘A shake-table experiment on pile foundations in liquefi able soils composed of liquefi able sand and overlying soft clay is studied. A three-dimensional(3D) effective stress fi nite element(FE) analysis is employed to simulate the experiment. A recently developed multi-surface elasto-plastic constitutive model and a fully coupled dynamic inelastic FE formulation(u-p) are used to model the liquefaction behavior of the sand. The soil domains are discretized using a solid-fl uid fully coupled(u-p) 20-8 noded brick element. The pile is simulated using beam-column elements. Upon careful calibration, very good agreement is obtained between the computed and the measured dynamic behavior of the ground and the pile. A parametric analysis is also conducted on the model to investigate the effect of pile-pinning, pile diameter, pile stiffness, ground inclination angle, superstructure mass and pile head restraints on the ground improvement. It is found that the pile foundation has a noticeable pinning effect that reduces the lateral soil displacement. It is observed that a larger pile diameter and fi xed pile head restraints contribute to decreasing the lateral pile deformation; however, a higher ground inclination angle tends to increase the lateral pile head displacements and pile stiffness, and superstructure mass seems to effectively infl uence the lateral pile displacements.
基金Project supported by the National Natural Science Foundation of China (Grant No.10271074)the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘An interval Pade-type approximation is introduced and then Routh-Pade-type method (IRPTM) is presented to model reduction in interval systems. The denominator in reduced model is obtained from the stable Routh table, and its numerator is constructed by the interval Pade-type definition. Compared to the existing Routh-Pade method, IRPTM does not need to solve linear interval equations theoretical analysis shows that IRPTM has example is given to illustrate our method. Hence, we do not have to compute smaller computational cost than that interval division in the process. Moreover, of Routh-Pade method. A typical numerical