A New Multidimensional Time Series Forecasting Method Based on the EOF Iteration Scheme

In this paper a new .mnultidimensional time series forecasting scheme based on the empirical orthogonal function (EOF) stepwise iteration process is introduced. The scheme is tested in a series of forecast experiments of Nino3 SST anomalies and Tahiti-Darwin SO index. The results show that the scheme is feasible and ENSO predictable.

Four-Step Iteration Scheme to Approximate Fixed Point for Weak Contractions

Fixed point theory is one of the most important subjects in the setting of metric spaces since fixed point theorems can be used to determine the existence and the uniqueness of solutions of such mathematical problems.It is known that many problems in applied sciences and engineering can be formulated as functional equations.Such equations can be transferred to fixed point theorems in an easy manner.Moreover,we use the fixed point theory to prove the existence and uniqueness of solutions of such integral and differential equations.Let X be a non-empty set.A fixed point for a self-mapping T on X is a point𝑒𝑒∈𝑋𝑋that satisfying T e=e.One of the most challenging problems in mathematics is to construct some iterations to faster the calculation or approximation of the fixed point of such problems.Some mathematicians constructed and generated some new iteration schemes to calculate or approximate the fixed point of such problems such as Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Berinde(2004b);Agarwal,O’Regan and Sahu(2007)].The main purpose of the present paper is to introduce and construct a new iteration scheme to calculate or approximate the fixed point within a fewer number of steps as much as we can.We prove that our iteration scheme is faster than the iteration schemes given by Sintunavarat et al.[Sintunavarat and Pitea(2016);Agarwal,O’Regan and Sahu(2007);Mann(1953);Ishikawa(1974)].We give some numerical examples by using MATLAB to compare the efficiency and effectiveness of our iterations scheme with the efficiency of Mann et al.[Mann(1953);Ishikawa(1974);Sintunavarat and Pitea(2016);Abbas and Nazir(2014);Agarwal,O’Regan and Sahu(2007)]schemes.Moreover,we introduce a problem raised from Newton’s law of cooling as an application of our new iteration scheme.Also,we support our application with a numerical example and figures to illustrate the validity of our iterative scheme.

Higher Order Iteration Schemes for Unconstrained Optimization

Using a predictor-corrector tactic, this paper derives new iteration schemes for unconstrained optimization. It yields a point (predictor) by some line search from the current point;then with the two points it constructs a quadratic interpolation curve to approximate some ODE trajectory;it finally determines a new point (corrector) by searching along the quadratic curve. In particular, this paper gives a global convergence analysis for schemes associated with the quasi-Newton updates. In our computational experiments, the new schemes using DFP and BFGS updates outperformed their conventional counterparts on a set of standard test problems.

Weak and strong convergence of an explicit iteration scheme with perturbed mapping for nonexpansive mappings

In this paper, we consider an explicit iteration scheme with perturbed mapping for nonexpansive mappings in real q-uniformly smooth Banach spaces. Some weak and strong convergence theorems for this explicit iteration scheme are established. In particular, necessary and sufficient conditions for strong convergence of this explicit iteration scheme are obtained. At last, some useful corollaries for strong convergence of this explicit iteration scheme are given.

建筑智能化系统顶层设计方法探讨

通过自上而下地展开,吸收质量功能配置的思想,对建设过程中影响智能化系统的因素进行统筹考量。通过逐层迭代的方式,直观展示不同技术方案对业主满意度的影响,为建筑设计提供可比较的方案效益评价,也为设计明确后续技术路径。

Data-Driven Active Disturbance Rejection Control of Plant-Protection Unmanned Ground Vehicle Prototype: A Fuzzy Indirect Iterative Learning Approach

Dear Editor,This letter proposes a fuzzy indirect iterative learning(FIIL)active disturbance rejection control(ADRC)scheme to address the impact of uncertain factors of plant-protection unmanned ground vehicle(UGV),in which ADRC is a data-driven model-free control algorithm that only relies on the input and output data of the system.Based on the established nonlinear time-varying dynamic model including dynamic load(medicine box),the FIIL technology is adopted to turn the bandwidth and control channel gain online,in which the fuzzy logic system is used to update the gain parameters of iterative learning in real time.Simulation and experiment show the FIIL-ADRC scheme has better control performance.

椭圆方程五点格式的迭代法与快速算法的比较

主要讨论在椭圆方程五点格式的问题中,分别使用Gauss-Seidel迭代法与快速Poisson算法对其求解,并对二者求解该线性方程组的速度进行比较。在系数矩阵是稀疏的大型线性方程组中,迭代法是一个很好的求解该类型的算法,主要是因为给定一个初始向量,通过一定的迭代公式,可以求得之后任意一次迭代的结果,且运算简便,但是,对于迭代法所求得的近似解是否收敛于精确解,并且,在线性方程组有快速算法的情况下,迭代法是否还能在求解方程组中占优势,还需进一步比较。通过比较不同的系数、不同的步长[λ]以及不同的误差要求,来判断Gauss-Seidel迭代法与快速Poisson算法的优劣。

Existence and iteration of monotone positive solutions for a third-order two-point boundary value problem

The existence of nondecreasing positive solutions for the nonlinear third-order twopoint boundary value problem u′″（t） ＋ q（t）f（t,u（t）,u′（t）） = 0, 0 〈 t 〈 1, u（0） = u″（0） = u′（1） = 0 is studied. The iterative schemes for approximating the solutions are obtained by applying a monotone iterative method.

Optimized finite difference iterative scheme based on POD technique for 2D viscoelastic wave equation

This study develops an optimized finite difference iterative （OFDI） scheme for the two-dimensional （2D） viscoelastic wave equation. The OFDI scheme is obtained using a proper orthogonal decomposition （POD） method. It has sufficiently high accuracy with very few unknowns for the 2D viscoelastic wave equation. Existence, stability, and convergence of the OFDI solutions are analyzed. Numerical simulations verify efficiency and feasibility of the proposed scheme.

Multistage Numerical Picard Iteration Methods for Nonlinear Volterra Integral Equations of the Second Kind

Using the Picard iteration method and treating the involved integration by numerical quadrature formulas, we propose a numerical scheme for the second kind nonlinear Volterra integral equations. For enlarging the convergence region of the Picard iteration method, multistage algorithm is devised. We also introduce an algorithm for problems with some singularities at the limits of integration including fractional integral equations. Numerical tests verify the validity of the proposed schemes.

Strong Convergence of an Implicit Iteration Process for a Finite Family of Asymptotically Ф-pseudocontractive Mappings

Strong convergence theorems for approximation of common fixed points of asymptotically Ф-quasi-pseudocontractive mappings and asymptotically C-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new composite implicit iteration scheme with errors. The results presented in this paper extend and improve the main results of Sun, Gu and Osilike published on J. Math. Anal. Appl.

Combined iterative cross-correlation demodulation scheme for mixing space borne automatic identification system signals

Aiming at the potential presence of mixing automatic identification system(AIS) signals,a new demodulation scheme was proposed for separating other interfering signals in satellite systems.The combined iterative cross-correlation demodulation scheme,referred to as CICCD,yielded a set of single short signals based on the prior information of AIS,after the frequency,code rate and modulation index were estimated.It demodulates the corresponding short codes according to the maximum peak of cross-correlation,which is simple and easy to implement.Numerical simulations show that the bit error rate of proposed algorithm improves by about 40% compared with existing ones,and about 3 dB beyond the standard AIS receiver.In addition,the proposed demodulation scheme shows the satisfying performance and engineering value in mixing AIS environment and can also perform well in low signal-to-noise conditions.

A Data-Adaptive Filter of the Tahiti-Darwin Southern Oscillation Index and the Associate Scheme of Filling Data Gaps

The Tahiti-Darwin Southern Oscillation index provided by Climate Analysis Center of USA has been used in numerous studies. But, it has some deficiency. It contains noise mainly due to high month-to-month variability. In order to reduce the level of noise in the SO index, this paper introduces a fully data-adaptive filter based on singular spectrum analysis. Another interesting aspect of the filter is that it can be used to fill data gaps of the SO index by an iterative process. Eventually, a noiseless long-period data series without any gaps is obtained.

A New Scheme for Discrete HJB Equations

In this paper we propose a relaxation scheme for solving discrete HJB equations based on scheme II [1] of Lions and Mercier. The convergence of the new scheme has been established. Numerical example shows that the scheme is efficient.

Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces

In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive operators in Banach spaces. We show that for the aforementioned class of operators, the CR iterative scheme is equivalent to and faster than Picard, Mann, Ishikawa, Agarwal et al., Noor and SP iterative schemes. Moreover, we also present various numerical examples using computer programming in C++ for the CR iterative scheme to compare it with the other above mentioned iterative schemes. Our results show that as far as the rate of convergence is concerned 1) for increasing functions the CR iterative scheme is best, while for decreasing functions the SP iterative scheme is best;2) CR iterative scheme is best for a certain class of quasi-contractive operators.

Comparison of Liquid Water Content Retrievals for Airborne Millimeter-Wave Radar with Different Particle Parameter Schemes

In the application of the physical iterative method to retrieve millimeter-wave radar liquid water content(LWC)and liquid water path(LWP),particle parameter scheme is the main factor affecting retrieval performance.In this paper,synchronous measurements of an airborne millimeter-wave radar and a hot-wire probe in stratus cloud are used to compare the LWC retrievals of the oceanic and continental particle parameter scheme with diameter less than 50μm and the particle parameter scheme with diameter less than 500μm and 1500μm(scheme 1,scheme 2,scheme 3,and scheme4,respectively).The results show that the particle parameter scheme needs to be selected according to the reflectivity factor when using the physical iterative method to retrieve the LWC and LWP.When the reflectivity factor is less than-30 d BZ,the retrieval error of scheme 1 is the minimum.When the reflectivity factor is greater than-30 d BZ,the retrieval error of scheme 4 is the minimum.Based on the reflectance factor value,the LWP retrievals of scheme 4 are closer to the measurements,the average relative bias is 5.2%,and the minimum relative bias is 4.4%.Compared with other schemes,scheme 4 seems to be more useful for the LWC and LWP retrieval of stratus cloud in China.

Two Energy-Preserving Compact Finite Difference Schemes for the Nonlinear Fourth-Order Wave Equation

In this paper,two fourth-order compact finite difference schemes are derived to solve the nonlinear fourth-order wave equation which can be viewed as a generalized model from the nonlinear beam equation.Differing from the existing compact finite difference schemes which preserve the total energy in a recursive sense,the new schemes are proved to per-fectly preserve the total energy in the discrete sense.By using the standard energy method and the cut-off function technique,the optimal error estimates of the numerical solutions are established,and the convergence rates are of O(h^(4)+τ^(2))with mesh-size h and time-step τ.In order to improve the computational efficiency,an iterative algorithm is proposed as the outer solver and the double sweep method for pentadiagonal linear algebraic equations is introduced as the inner solver to solve the nonlinear difference schemes at each time step.The convergence of the iterative algorithm is also rigorously analyzed.Several numerical results are carried out to test the error estimates and conservative properties.

TRANSONIC FLOW CALCULATION OF EULER EQUATIONS BY IMPLICIT ITERATING SCHEME WITH FLUX SPLITTING

Three dimensional Euler equations are solved in the finite volume form with van Leer's flux vector splitting technique. Block matrix is inverted by Gauss-Seidel iteration in two dimensional plane while strongly implicit alternating sweeping is implemented in the direction of the third dimension. Very rapid convergence rate is obtained with CFL number reaching the order of 100. The memory resources can be greatly saved too. It is verified that the reflection boundary condition can not be used with flux vector splitting since it will produce too large numerical dissipation. The computed flow fields agree well with experimental results. Only one or two grid points are there within the shock transition zone.

基于几何建模与仿真模拟的无人机无源定位模型

主要研究无人机纯方位无源定位,建立定位模型和调整方案模型,完成有效定位被动接收信号无人机以及进行纯方位无源定位调整工作.根据建模赛题给出的案例,本文首先采用正弦定理推导出具体定位方案,再采用分步调整法制定无人机编队调整方案,最后为锥形编队制定同心圆结构,并沿用定位、调整方案建立锥形编队的定位模型.利用网格搜索、迭代、仿真模拟等算法求解得到结果,然后结合实际给出结果的合理性、适用性检验说明,最后对小组研究模型进行总结.

迭代Faster R-CNN的密集行人检测

行人检测是利用计算机视觉技术判断图像或者视频序列中是否存在行人并给予精确定位。针对行人检测在密集场景下普遍存在的行人间遮挡问题,提出基于迭代Faster R-CNN的密集行人检测模型,利用一种IterDet迭代方案对Faster R-CNN进行改进,有效解决非极大值抑制(NMS)算法及其改进在选择精确度和召回率之间平衡点的难题。同时利用递归金字塔结构(RFP)进一步增强模型提取特征能力。在具有挑战性的WiderPerson和CrowdHuman数据集上进行训练和验证,实验结果表明,该模型相比Faster R-CNN在精度和召回率显著提升的同时,漏检率也明显降低。尤其在WiderPerson数据集上召回率、精度、漏检率等性能指标分别达到了97.65%、91.29%、40.43%的SOTA结果。