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A NEW ALGORITHM FOR COMPUTING THE INVERSE AND GENERALIZED INVERSE OF THE SCALED FACTOR CIRCULANT MATRIX 被引量:2
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作者 Zhaolin Jiang Zongben Xu 《Journal of Computational Mathematics》 SCIE CSCD 2008年第1期112-122,共11页
A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid's algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the sing... A new algorithm for finding the inverse of a nonsingular scaled factor circulant matrix is presented by the Euclid's algorithm. Extension is made to compute the group inverse and the Moore-Penrose inverse of the singular scaled factor circulant matrix. Numerical examples are presented to demonstrate the implementation of the proposed algorithm. 展开更多
关键词 Scaled factor circulant matrix INVERSE Group inverse Moore-Penrose inverse
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A quantum algorithm for Toeplitz matrix-vector multiplication
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作者 高尚 杨宇光 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第10期248-253,共6页
Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quant... Toeplitz matrix-vector multiplication is widely used in various fields,including optimal control,systolic finite field multipliers,multidimensional convolution,etc.In this paper,we first present a non-asymptotic quantum algorithm for Toeplitz matrix-vector multiplication with time complexity O(κpolylogn),whereκand 2n are the condition number and the dimension of the circulant matrix extended from the Toeplitz matrix,respectively.For the case with an unknown generating function,we also give a corresponding non-asymptotic quantum version that eliminates the dependency on the L_(1)-normρof the displacement of the structured matrices.Due to the good use of the special properties of Toeplitz matrices,the proposed quantum algorithms are sufficiently accurate and efficient compared to the existing quantum algorithms under certain circumstances. 展开更多
关键词 quantum algorithm Toeplitz matrix-vector multiplication circulant matrix
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Minimum Cycle of Row Vector of a Generalized Circulant Fuzzy Matrix
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作者 冼国荣 陈卓荣 《Chinese Quarterly Journal of Mathematics》 CSCD 1997年第1期104-110, ,共7页
In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some propert... In this paper,we intreduce the concept and discuss the properties of minimum cycle of row vector in a generalized circulant Fuzzy matrix. We present a new expression for circulant Fuzzy matrix,and discuss some properties of the idempotent elements of the semigroup of generalized circulant Fuzzy matrixes in connection with minimum cycle of row vector. 展开更多
关键词 generalized circulant Fuzzy matrix SEMIGROUP VECTOR CYCLE idempotent element
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EIGENVALUES OF A SPECIAL KIND OF SYMMETRIC BLOCK CIRCULANT MATRICES 被引量:3
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作者 WangLigong LiXueliang HoedeC 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2004年第1期17-26,共10页
In this paper, the spectrum and characteristic polynomial for a special kind of symmetric block circulant matrices are given.
关键词 block circulant matrix EIGENVALUE characteristic polynomial integr al graph.
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ONTHEPROPERTIESOFZCIRCULANTMATRICES
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作者 DING Xueren WANG Peili (Dept. of Mathematics) 《Transactions of Tianjin University》 EI CAS 1996年第1期91-93,共3页
Some properties of Z circulant matrices are given.
关键词 Z circulant matrix normal matrix square matric function
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The primitive matrices of sandwich semigroups of generalized circulant Boolean matrices
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作者 LIU Jian-ping CHEN Jin-song 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2013年第3期311-320,共10页
Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient condi... Let Gn(C) be the sandwich semigroup of generalized circulant Boolean matrices with the sandwich matrix C and Gc(Jr~) the set of all primitive matrices in Gn(C). In this paper, some necessary and sufficient conditions for A in the semigroup Gn(C) to be primitive are given. We also show that Gc(Jn) is a subsemigroup of Gn(C). 展开更多
关键词 generalized circulant Boolean matrix sandwich semigroup primitive matrix.
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Half Rate Quasi Cyclic Low Density Parity Check Codes Based on Combinatorial Designs 被引量:2
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作者 Sina Vafi Narges Rezvani Majid 《Journal of Computer and Communications》 2016年第12期39-49,共12页
This paper presents new half rate Quasi Cyclic Low Density Parity Check (QC- LDPC) codes formed on the basis of combinatorial designs. In these codes, circulant matrices of the parity check matrix are formed on the ba... This paper presents new half rate Quasi Cyclic Low Density Parity Check (QC- LDPC) codes formed on the basis of combinatorial designs. In these codes, circulant matrices of the parity check matrix are formed on the basis of subsets in which the difference between any two elements of a subset is unique with all differences obtained from the same or different subsets. This structure of circulant matrices guarantees non-existence of cycle-4 in the Tanner graph of QC-LDPC codes. First, an irregular code with girth 6 constituted by two rows of circulant matrices is proposed. Then, more criteria will be considered on the structure of subsets with the mentioned feature aiming to represent a new scheme of regular QC-LPDC codes with girth at least 8. From simulations, it is confirmed that codes have similar to or better performance than other well-known half rate codes, while require lower complexity in their design. 展开更多
关键词 Quasi-Cyclic LDPC Codes Combinatorial Designs circulant matrix
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Isomorphisms of Cubic Cayley Graphs on Dihedral Groups and Sparse Circulant Matrices
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作者 Istvan KOVACS 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2023年第4期618-632,共15页
We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cu... We show that,up to isomorphism,there is a unique non-CI connected cubic Cayley graph on the dihedral group of order 2n for each even number n≥4.This answers in the negative the question of Li whether all connected cubic Cayley graphs are CI-graphs(Discrete Math.,256,301-334(2002)).As an application,a formula is derived for the number of isomorphism classes of connected cubic Cayley graphs on dihedral groups,which generalises the earlier formula of Huang et al.dealing with the particular case when n is a prime(Acta Math.Sin.,Engl.Ser.,33,996-1011(2017)).As another application,a short proof is also given for a result on sparse circulant matrices obtained by Wiedemann and Zieve(arXiv preprint,(2007)). 展开更多
关键词 Cayley graph graph isomorphism dihedral group circulant matrix
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Quantum quasi-cyclic low-density parity-check error-correcting codes 被引量:1
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作者 李渊 曾贵华 Moon Ho Leeb 《Chinese Physics B》 SCIE EI CAS CSCD 2009年第10期4154-4160,共7页
In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some ne... In this paper, we propose the approach of employing circulant permutation matrices to construct quantum quasicyclic (QC) low-density parity-check (LDPC) codes. Using the proposed approach one may construct some new quantum codes with various lengths and rates of no cycles-length 4 in their Tanner graphs. In addition, these constructed codes have the advantages of simple implementation and low-complexity encoding. Finally, the decoding approach for the proposed quantum QC LDPC is investigated. 展开更多
关键词 quantum LDPC code quasi-cycliC circulant permutation matrix CSS code
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Non-Blind Image Deblurring via Shear Total Variation Norm
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作者 LI Weiyu ZHANG Tao GAO Qiuli 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第3期219-227,共9页
In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domai... In this paper, we propose a novel shear gradient operator by combining the shear and gradient operators. The shear gradient operator performs well to capture diverse directional information in the image gradient domain. Based on the shear gradient operator, we extend the total variation(TV) norm to the shear total variation(STV) norm by adding two shear gradient terms. Subsequently, we introduce a shear total variation deblurring model. Experimental results are provided to validate the ability of the STV norm to capture the detailed information. Leveraging the Block Circulant with Circulant Blocks(BCCB) structure of the shear gradient matrices, the alternating direction method of multipliers(ADMM) algorithm can be used to solve the proposed model efficiently. Numerous experiments are presented to verify the performance of our algorithm for non-blind image deblurring. 展开更多
关键词 image deblurring shear total variation(STV)norm alternating direction method of multipliers(ADMM) Block circulant with circulant Blocks(BCCB)matrix
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STRUCTURES OF CIRCULANT INVERSE M-MATRICES
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作者 Yurui Lin Linzhang Lu 《Journal of Computational Mathematics》 SCIE EI CSCD 2007年第5期553-560,共8页
In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c(n- 1)] is not a positive matrix and ... In this paper, we present a useful result on the structures of circulant inverse Mmatrices. It is shown that if the n × n nonnegative circulant matrix A = Circ[c0, c1,… , c(n- 1)] is not a positive matrix and not equal to c0I, then A is an inverse M-matrix if and only if there exists a positive integer k, which is a proper factor of n, such that cjk 〉 0 for j=0,1…, [n-k/k], the other ci are zero and Circ[co, ck,… , c(n-k)] is an inverse M-matrix. The result is then extended to the so-called generalized circulant inverse M-matrices. 展开更多
关键词 Nonnegative matrices circulant matrix Inverse M-matrices.
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The Method of Fundamental Solutions for Solving Exterior Axisymmetric Helmholtz Problems with High Wave-Number
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作者 Wen Chen Ji Lin C.S.Chen 《Advances in Applied Mathematics and Mechanics》 SCIE 2013年第4期477-493,共17页
In this paper,we investigate the method of fundamental solutions(MFS)for solving exterior Helmholtz problems with high wave-number in axisymmetric domains.Since the coefficientmatrix in the linear system resulting fro... In this paper,we investigate the method of fundamental solutions(MFS)for solving exterior Helmholtz problems with high wave-number in axisymmetric domains.Since the coefficientmatrix in the linear system resulting fromtheMFS approximation has a block circulant structure,it can be solved by the matrix decomposition algorithm and fast Fourier transform for the fast computation of large-scale problems and meanwhile saving computer memory space.Several numerical examples are provided to demonstrate its applicability and efficacy in two and three dimensional domains. 展开更多
关键词 Method of fundamental solutions exterior Helmholtz problem circulant matrix fast Fourier transform axisymmetric domain
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PERIODIC CARDINAL INTERPOLATORY WAVELETS 被引量:6
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《Chinese Annals of Mathematics,Series B》 SCIE CSCD 1998年第2期133-142,共10页
关键词 Periodic wavelet MULTIRESOLUTION Cardinal Interpolation Dual basis circulant matrix
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Non-Blind Image Deblurring Method Using Shear High Order Total Variation Norm 被引量:1
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作者 LU Lixuan ZHANG Tao 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第6期495-506,共12页
In this paper,we propose a shear high-order gradient(SHOG)operator by combining the shear operator and high-order gradient(HOG)operator.Compared with the HOG operator,the proposed SHOG operator can incorporate more di... In this paper,we propose a shear high-order gradient(SHOG)operator by combining the shear operator and high-order gradient(HOG)operator.Compared with the HOG operator,the proposed SHOG operator can incorporate more directionality and detect more abundant edge information.Based on the SHOG operator,we extend the total variation(TV)norm to shear high-order total variation(SHOTV),and then propose a SHOTV deblurring model.We also study some properties of the SHOG operator,and show that the SHOG matrices are Block Circulant with Circulant Blocks(BCCB)when the shear angle isπ/4.The proposed model is solved efficiently by the alternating direction method of multipliers(ADMM).Experimental results demonstrate that the proposed method outperforms some state-of-the-art non-blind deblurring methods in both objective and perceptual quality. 展开更多
关键词 image deblurring high-order TV norm Block circulant with circulant Blocks(BCCB)matrix shear operator alternating direction method of multipliers(ADMM)
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