A Self-calibration Bundle Adjustment Algorithm Based on Block Matrix Cholesky Decomposition Technology

In this study,the problem of bundle adjustment was revisited,and a novel algorithm based on block matrix Cholesky decomposition was proposed to solve the thorny problem of self-calibration bundle adjustment.The innovation points are reflected in the following aspects:①The proposed algorithm is not dependent on the Schur complement,and the calculation process is simple and clear;②The complexities of time and space tend to O(n)in the context of world point number is far greater than that of images and cameras,so the calculation magnitude and memory consumption can be reduced significantly;③The proposed algorithm can carry out self-calibration bundle adjustment in single-camera,multi-camera,and variable-camera modes;④Some measures are employed to improve the optimization effects.Experimental tests showed that the proposed algorithm has the ability to achieve state-of-the-art performance in accuracy and robustness,and it has a strong adaptability as well,because the optimized results are accurate and robust even if the initial values have large deviations from the truth.This study could provide theoretical guidance and technical support for the image-based positioning and 3D reconstruction in the fields of photogrammetry,computer vision and robotics.

A Novel Approach to Practical Matrix Converter Motor Drive System With Reverse Blocking IGBT

a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)

A Novel Approach to Practical Matrix Converter Motor Drive System With Reverse Blocking IGBT (To continue)

a Pole voltage waveforms (VA20 and VA40) for modulation index 0.4 (middle trace is A-phase voltage waveform) x-axis: 1 div.=10ms, y-axis: 1 div.= 100V b Normalized harmonic spectrum for pole voltage of Fig. 9a c A-phase current and phase voltage for modulation index 0.4 (reference space vector is in inner layer)

RUAP:Random Rearrangement Block Matrix-Based Ultra-Lightweight RFID Authentication Protocol for End-Edge-Cloud Collaborative Environment

Cloud computing provides powerful processing capabilities for large-scale intelligent Internet of things(IoT)terminals.However,the massive realtime data processing requirements challenge the existing cloud computing model.The edge server is closer to the data source.The end-edge-cloud collaboration offloads the cloud computing tasks to the edge environment,which solves the shortcomings of the cloud in resource storage,computing performance,and energy consumption.IoT terminals and sensors have caused security and privacy challenges due to resource constraints and exponential growth.As the key technology of IoT,Radio-Frequency Identification(RFID)authentication protocol tremendously strengthens privacy protection and improves IoT security.However,it inevitably increases system overhead while improving security,which is a major blow to low-cost RFID tags.The existing RFID authentication protocols are difficult to balance overhead and security.This paper designs an ultra-lightweight encryption function and proposes an RFID authentication scheme based on this function for the end-edge-cloud collaborative environment.The BAN logic proof and protocol verification tools AVISPA formally verify the protocol’s security.We use VIVADO to implement the encryption function and tag’s overhead on the FPGA platform.Performance evaluation indicates that the proposed protocol balances low computing costs and high-security requirements.

Exact Inversion of Pentadiagonal Matrix for Semi-Analytic Solution of 2D Poisson Equation

This work essentially consists in inverting in an exact, explicit, and original way the pentadiagonal Toeplitz matrix or tridiagonal block matrix resulting from the discretization of the two-dimensional Laplace operator. This method is an algorithm facilitating the resolution of a large number of problems governed by PDEs involving the Laplacian in two dimensions. It guarantees high precision and high efficiency in solving various differential equations.

Determination of the early Paleozoic accretionary complex in Southwestern Yunnan, China: Implications for the tectonic evolution of the Proto-Tethys Ocean

Accretionary complex study provides important knowledge on the subduction and the geodynamic processes of the oceanic plate,which represents the ancient ocean basin extinction location.Nevertheless,there exist many disputes on the age,material source,and tectonic attribute of the Lancang Group,located in Southwest Yunnan,China.In this paper,the LA-ICP-MS detrital zircon U‒Pb chronology of nine metamorphic rocks in the Lancang Group was carried out.The U‒Pb ages of the three detrital zircons mainly range from 590-550 Ma,980-910 Ma,and 1150-1490 Ma,with the youngest detrital zircons having a peak age of about 560 Ma.The U‒Pb ages of the six detrital zircons mainly range from 440-460 Ma and 980-910 Ma,and the youngest detrital zircon has a peak age of about 445 Ma.In the Lancang Group,metamorphic acidic volcanic rocks,basic volcanic rocks,intermediate-acid intrusive rocks,and high-pressure metamorphic rocks are exposed in the form of tectonic lens in schist,rendering typical melange structural characteristics of“block+matrix”.Considering regional deformation and chronology,material composition characteristics,and the previous data,this study thinks the Lancang Group may be an early Paleozoic tectonic accretionary complex formed by the eastward subduction of the Changning-Menglian Proto-Tethys Ocean,which provides an important constraint for the Tethys evolution.

一个2×2块矩阵的Moore-Penrose逆的显式公式

The representation for the Moore-Penrose inverse of the matrix[AC BD]is derived by using the solvability theory of linear equations,where A∈C^(m×n),B∈C^(m×p),C∈C^(q×n)and D∈C^(q×p),with which some special cases are discussed.

An interference suppression algorithm for cognitive bistatic airborne radars

Interference suppression is a challenge for radar researchers, especially when mainlobe and sidelobe interference coexist. We present a comprehensive anti-interference approach based on a cognitive bistatic airborne radar. The risk of interception is reduced by lowering the launch energy of the radar transmitting terminal in the direction of interference;main lobe and sidelobe interferences are suppressed via cooperation between the two radars. The interference received by a single radar is extracted from the overall radar signal using multiple signal classification(MUSIC), and the interference is cross-located using two different azimuthal angles. Neural networks allowing good, non-linear nonparametric approximations are used to predict the location of interference, and this information is then used to preset the transmitting notch antenna to reduce the likelihood of interception. To simultaneously suppress mainlobe and sidelobe interferences, a blocking matrix is used to mask mainlobe interference based on azimuthal information, and an adaptive process is used to suppress sidelobe interference. Mainlobe interference is eliminated using the data received by the two radars. Simulation verifies the performance of the model.

Construction and Analysis of Structured Preconditioners for Block Two-by-Two Matrices

For the large sparse block two-by-two real nonsingular matrices, we establish a general framework of structured preconditioners through matrix transformation and matrix approximations. For the specific versions such as modified block Jacobi-type, modified block Gauss-Seidel-type, and modified block unsymmetric (symmetric) Gauss-Seidel-type preconditioners, we precisely describe their concrete expressions and deliberately analyze eigenvalue distributions and positive definiteness of the preconditioned matrices. Also, we show that when these structured preconditioners are employed to precondition the Krylov subspace methods such as GMRES and restarted GMRES, fast and effective iteration solvers can be obtained for the large sparse systems of linear equations with block two-by-two coefficient matrices. In particular, these structured preconditioners can lead to high-quality preconditioning matrices for some typical matrices from the real-world applications.

EIGENVALUES OF A SPECIAL KIND OF SYMMETRIC BLOCK CIRCULANT MATRICES

In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.

Furi-Martelli-Vignoli spectrum and Feng spectrum of nonlinear block operator matrices

We investigate the Furi-Martelli-Vignoli spectrum and the Feng spectrum of continuous nonlinear block operator matrices,and mainly describe the relationship between the Furi-Martelli-Vignoli spectrum(compared to the Feng spectrum)of the whole operator matrix and that of its entries.In addition,the connection between the Furi-Martelli-Vignoli spectrum of the whole operator matrix and that of its Schur complement is presented by means of Schur decomposition.

YAMDROK MELANGE,SOUTH TIBET

Yamdrok melange occurs south of, and parallel to, the Yarlung—Zangbo ophiolites, extending several hundreds of kilometres with a width of several to tens of kilometres. Areas near Baisa and Rilang in the Gyangze district were chosen for detailed investigation in this study. Three months of field mapping (1∶1000 and 1∶50000) has been followed by laboratory investigation to extract radiolarians from cherty blocks and matrix material. Laboratory work is continuing..Field investigations in the Baisa area near Gyangze indicate the presence of three melange facies:broken formation, matrix\|rich facies, and block\|in\|matrix melange. Broken formation is characterized by disruption of layering by means of boudinage and pinching\|and\|swelling and dispersal of blocks within the finer\|grained shales due to layer\|parallel extension. Broken formation occurs mostly as dispersed but more\|or\|less traceable lenses within a foliated matrix. A transition from broken formation to typical block\|in\|matrix melange is observed in the field. Further disruption of broken formation leads to the formation of typical block\|in\|matrix melange either, by later shearing, or by suspected mud diapirism. Matrix\|rich facies is characterized by a dominance of shale matrix containing small granules of sandstone and other lithologies. This facies commonly is subject to later deformation, with disruption of the primary foliation into sigmoidal structures. Block\|in\|matrix facies is the most common melange facies and is characterized by blocks of different sizes, shapes and lithologies either encased in, or floating on, relatively finer\|grained arenaceous\|argillaceous matrix. Blocks range in size from several centimeters to several hundreds of meters, and have various shapes from phacoidal, elongate, to irregular. The blocks are mainly composed of varicolored cherts, greywacke and limestone as well as igneous rocks including serpentinite and basalt breccia. The matrix is mainly composed of dark argillaceous shales and siliceous shales, and partly of yellowish green greywacke. The injection or intrusion of mud matrix into blocks is quite common in this melange facies.

THE EXPONENTIAL OF QUASI BLOCK-TOEPLITZ MATRICES

The matrix Wiener algebra,W_(N):=M_(N)(W)of order N>0,is the matrix algebra formed by N×N matrices whose entries belong to the classical Wiener algebraWof functions with absolutely convergent Fourier series.A block-Toeplitz matrix T(a)=[A_(i,j)]i,j≥0is a block semi-infinite matrix such that its blocks A_(i,j) are finite matrices of order N,A_(i,j)=A^(r,s) whenever i-j=r-s and its entries are the coefficients of the Fourier expansion of the generator a:T→M_(N)(C).Such a matrix can be regarded as a bounded linear operator acting on the direct sum of N copies of L^(2)(T).We show that exp(T(a))differes from T(exp(a))only in a compact operator with a known bound on its norm.In fact,we prove a slightly more general result:for every entire function f and for every compact operator E,there exists a compact operator F such that f(T(a)+E)=T(f(a))+F.We call these T(a)+E′s matrices,the quasi block-Toeplitz matrices,and we show that via a computation-friendly norm,they form a Banach algebra.Our results generalize and are motivated by some recent results of Dario Andrea Bini,Stefano Massei and Beatrice Meini.

A note on“Block H-matrices and spectrum of block matrices”

In this paper, we make further discussions and improvements on the results presented in the previously published work ＂Block H-matrices and spectrum of block matrices＂. Furthermore, a new bound for eigenvalues of block matrices is given with examples to show advantages of the new result.

A NOTE ON THE REPRESENTATIONS FOR THE GENERALIZED DRAZIN INVERSE OF BLOCK MATRICES

We present some representations for the generalized Drazin inverse of a block matrix x =[cd ab]in a Banach algebra ~4 in terms of ad and （be）d under certain conditions,extending some recent result related to the generalized Drazin inverse of an anti-triangular operator matrix. Also, several particular cases of this result are considered.

Some additive results on Drazin inverse

In this paper, we investigate additive results of the Drazin inverse of elements in a ring R. Under the condition ab = ha, we show that a ＋ b is Drazin invertible if and only if aaD （a ＋ b） is Drazin invertible, where the superscript D means the Drazin inverse. Furthermore we find an expression of （a ＋ b）D. As an application we give some new representations for the Drazin inverse of a 2 × 2 block matrix.

2×2分块矩阵群逆的表示（英文）

In this paper, we present a method how to get the expression for the group inverse of 2×2 block matrix and get the explicit expressions of the block matrix (A C B D) under some conditions.

An Efficient Construction of Secure Network Coding

Under the assumption that the wiretapper can get at most r(r < n) independent messages, Cai et al. showed that any rate n multicast code can be modified to another secure network code with transmitting rate n- r by a properly chosen matrix Q^(-1). They also gave the construction for searching such an n × n nonsingular matrix Q. In this paper, we find that their method implies an efficient construction of Q. That is to say, Q can be taken as a special block lower triangular matrix with diagonal subblocks being the(n- r) ×(n- r)and r × r identity matrices, respectively. Moreover, complexity analysis is made to show the efficiency of the specific construction.

Space-Fractional Diffusion with Variable Order and Diffusivity:Discretization and Direct Solution Strategies

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order.Significant computational challenges are encoun-tered when solving these equations due to the kernel singularity in the fractional integral operator and the resulting dense discretized operators,which quickly become prohibitively expensive to handle because of their memory and arithmetic complexities.In this work,we present a singularity-aware discretization scheme that regularizes the singular integrals through a singularity subtraction technique adapted to the spatial variability of diffusiv-ity and fractional order.This regularization strategy is conveniently formulated as a sparse matrix correction that is added to the dense operator,and is applicable to different formula-tions of fractional diffusion equations.We also present a block low rank representation to handle the dense matrix representations,by exploiting the ability to approximate blocks of the resulting formally dense matrix by low rank factorizations.A Cholesky factorization solver operates directly on this representation using the low rank blocks as its atomic com-putational tiles,and achieves high performance on multicore hardware.Numerical results show that the singularity treatment is robust,substantially reduces discretization errors,and attains the first-order convergence rate allowed by the regularity of the solutions.They also show that considerable savings are obtained in storage(O(N^(1.5)))and computational cost(O(N^(2)))compared to dense factorizations.This translates to orders-of-magnitude savings in memory and time on multidimensional problems,and shows that the proposed methods offer practical tools for tackling large nonlocal fractional diffusion simulations.

The Insphere of a Tetrahedron

A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.