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本文给出了r-分块循环矩阵的概念,并利用矩阵的张量积探讨了r-分块循环矩阵的相似类及其对角化问题,得出了一些重要的结论. 相似文献
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两个分块矩阵相似性的研究 总被引:1,自引:1,他引:0
程士珍 《数学的实践与认识》2005,35(3):191-194
给出两个分块矩阵相似的两个充分必要条件 .也就是说 ,如果两个方阵 A和 B在 A2 =0和 B2 =0的条件下 ,则两个分块矩阵 A C0 B 和 A 00 B 相似的充分必要条件是 :rank A C0 B =rank(A) +rank(B)和 AC +CB =0 .如果两个方阵 A和 B在 A2 =A和 B2 =B的条件下 ,则两个分块矩阵 A C0 B和 A 00 B 相似的充分必要条件是 :AC +CB =C. 相似文献
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相似变换矩阵的简单求法 总被引:3,自引:1,他引:3
在研究矩阵相似问题时,如果知道矩阵A及相似变换矩阵P,则可求出与A相似的矩阵B=P~(-1)AP 反过来,如果知道A及其相似矩阵B,如何求相似变换矩阵P的问题,一般线性代数教材都很少提及它。即使个别教材中提到这个问题,也只是针对B是A的Jordan标准形的简单情形,应用解非齐次线性方程组AX=XB的方法求出相似变换矩阵P的,因B是特殊情形,所以这种方法不具有普遍意义。 相似文献
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1引言分块反循环矩阵在数值分析、优化理论、泛函微分方程、工程力学等学科领域有十分重要的应用,当今电子计算机及计算技术的迅速发展为分块反循环矩阵的应用开辟了更为广阔的前景.本文讨论了分块反循环矩阵的交换性、特征根及对角化问题,得到任一分块反循环矩阵可用一个正交矩阵组线性表示和基本分块反循环矩阵在复数域上可以对角化且相似于对角阵的结论. 相似文献
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An Algebraic Multigrid-Based Physical Factorization Preconditioner for the Multi-Group Radiation Diffusion Equations in Three Dimensions
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The paper investigates the robustness and parallel scaling properties of
a novel physical factorization preconditioner with algebraic multigrid subsolves in
the iterative solution of a cell-centered finite volume discretization of the three-dimensional multi-group radiation diffusion equations. The key idea is to take advantage of a particular kind of block factorization of the resulting system matrix and
approximate the left-hand block matrix selectively spurred by parallel processing
considerations. The spectral property of the preconditioned matrix is then analyzed.
The practical strategy is considered sequentially and in parallel. Finally, numerical results illustrate the numerical robustness, computational efficiency and parallel
strong and weak scalabilities over the real-world structured and unstructured coupled problems, showing its competitiveness with many existing block preconditioners. 相似文献
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We present a block algorithm for computing rank-revealing QR factorizations (RRQR factorizations) of rank-deficient matrices. The algorithm is a block generalization of the RRQR-algorithm of Foster and Chan. While the unblocked algorithm reveals the rank by peeling off small singular values one by one, our algorithm identifies groups of small singular values. In our block algorithm, we use incremental condition estimation to compute approximations to the nullvectors of the matrix. By applying another (in essence also rank-revealing) orthogonal factorization to the nullspace matrix thus created, we can then generate triangular blocks with small norm in the lower right part ofR. This scheme is applied in an iterative fashion until the rank has been revealed in the (updated) QR factorization. We show that the algorithm produces the correct solution, under very weak assumptions for the orthogonal factorization used for the nullspace matrix. We then discuss issues concerning an efficient implementation of the algorithm and present some numerical experiments. Our experiments show that the block algorithm is reliable and successfully captures several small singular values, in particular in the initial block steps. Our experiments confirm the reliability of our algorithm and show that the block algorithm greatly reduces the number of triangular solves and increases the computational granularity of the RRQR computation.This work was supported by the Applied Mathematical Sciences subprogram of the Office of Energy Research, US Department of Energy, under Contract W-31-109-Eng-38. The second author was also sponsored by a travel grant from the Knud Højgaards Fond.This work was partially completed while the author was visiting the IBM Scientific Center in Heidelberg, Germany. 相似文献
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引进了块复合矩阵的块C-特征值、块C-特征向量的概念,给出了块C-特征向量块线性无关的等价表征,并由此讨论了块复合幂零矩阵的性质,给出了这类矩阵的块C-特征向量块线性相关的等价表征. 相似文献
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Zhaolin Jiang Zongben Xu Shuping Gao 《高等学校计算数学学报(英文版)》2006,15(1):1-11
In this paper,algorithms for finding the inverse of a factor block circulant matrix, a factor block retrocirculant matrix and partitioned matrix with factor block circulant blocks over the complex field are presented respectively.In addition,two algorithms for the inverse of a factor block circulant matrix over the quaternion division algebra are proposed. 相似文献
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导出了对角因子分块循环矩阵的概念,把循环矩阵的对角化和谱分解推广到具有对角因子循环结构的分块矩阵中去. 相似文献
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In the framework of a special block alternating splitting implicit (BASI) iteration scheme for generalized saddle point problems, we establish some new iteration methods for solving double saddle point problems by means of a suitable partitioning strategy. Convergence analysis of the corresponding BASI iteration methods indicates that they are convergent unconditionally under certain weak requirements for the related matrix splittings, which are satisfied directly for our specific application to double saddle point problems. Numerical examples for liquid crystal director and time-harmonic eddy current models are presented to demonstrate the efficiency of the proposed BASI preconditioners to accelerate the GMRES method. 相似文献
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在文章中,作者给出了块三对角矩阵行列式的一些关系式,本文在,=三基础之上给出了此类矩阵一些类似的关系式. 相似文献
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It has been shown by Delosme and Morf that an arbitrary block matrix can be embedded into a block Toeplitz matrix; the dimension of this embedding depends on the complexity of the matrix structure compared to the block Toeplitz structure. Due to the special form of the embedding matrix, the algebra of matrix polynomials relative to block Toeplitz matrices can be interpreted directly in terms of the original matrix and therefore can be extended to arbitrary matrices. In fact, these polynomials turn out to provide an appropriate framework for the recently proposed generalized Levinson algorithm solving the general matrix inversion problem. 相似文献
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Yury J. Ionin 《Discrete Mathematics》2006,306(14):1557-1568
The first infinite families of symmetric designs were obtained from finite projective geometries, Hadamard matrices, and difference sets. In this paper we describe two general methods of constructing symmetric designs that give rise to the parameters of all other known infinite families of symmetric designs. The method of global decomposition produces an incidence matrix of a symmetric design as a block matrix with each block being a zero matrix or an incidence matrix of a smaller symmetric design. The method of local decomposition represents incidence matrices of a residual and a derived design of a symmetric design as block matrices with each block being a zero matrix or an incidence matrix of a smaller residual or derived design, respectively. 相似文献
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We firstly consider the block dominant degree for I-(II-)block strictly diagonally dominant matrix and their Schur complements, showing that the block dominant degree for the Schur complement of an I-(II-)block strictly diagonally dominant matrix is greater than that of the original grand block matrix. Then, as application, we present some disc theorems and some bounds for the eigenvalues of the Schur complement by the elements of the original matrix. Further, by means of matrix partition and the Schur complement of block matrix, based on the derived disc theorems, we give a kind of iteration called the Schur-based iteration, which can solve large scale linear systems though reducing the order by the Schur complement and the numerical example illustrates that the iteration can compute out the results faster. 相似文献