首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
本文重新论述有界灰方阵的非奇异性判别问题,提出“条件非奇异”与“最大非奇异子元值域”的新概念,指出现有结果的局限性,给出了一些实用判据,并对灰逆阵的存在性条件与定义域作了研究.此外,本文又提出有界灰矩阵的“灰秩”的新概念与算法,建立了有界灰矩阵恒满秩、恒不满秩、条件满秩的判据。  相似文献   

2.
关于非奇异性判别的Gudkov定理   总被引:2,自引:0,他引:2  
本文主要研究矩阵的非奇异性判别,推广了Szulc和李最近在该领域所取得的主要结果。  相似文献   

3.
对角占优矩阵奇异性研究   总被引:2,自引:0,他引:2  
本研究了对角占化矩阵的奇异性.得到了此类矩阵非奇异的一个筒单判断法.改进了已有结论。  相似文献   

4.
本文得出了上三角 Toeplitz 矩阵关于矩阵乘法构成一交换群的结果,并给出其逆矩阵的计算方法.  相似文献   

5.
上三角Toeplitz矩阵的一个结论   总被引:1,自引:1,他引:1  
赵建中 《工科数学》1999,15(3):148-150
本得出了上三角Toeplitz矩阵关于矩阵乘法构成一交换群的结果,并给出其逆矩阵的计算方法.  相似文献   

6.
针对有关“型”矩阵的三角分解问题 ,提出了一种 Toeplitz型矩阵的逆矩阵的快速三角分解算法 .首先假设给定 n阶非奇异矩阵 A,利用一组线性方程组的解 ,得到 A- 1的一个递推关系式 ,进而利用该关系式得到 A- 1的一种三角分解表达式 ,然后从 Toeplitz型矩阵的特殊结构出发 ,利用上述定理的结论 ,给出了Toeplitz型矩阵的逆矩阵的一种快速三角分解算法 ,算法所需运算量为 O( mn2 ) .最后 ,数值计算表明该算法的可靠性 .  相似文献   

7.
给出了分块 r-循环 Toeplitz矩阵特征方程的一个求法 ,推广了文 [1 ]的结果 .  相似文献   

8.
麦苗 《工科数学》2000,16(3):95-98
给出了分块r-循环Toeplitz矩阵特征方程的一个求法,推广了「1」的结果。  相似文献   

9.
徐仲  陆全 《工科数学》1999,15(1):81-83
Toeplitz矩阵Tn=(ti-j)n/i·j=0在信号处理、系统理论、逼近论、正交多项式.积分方程数值解等许多领域常常遇到,易知,Toeplitz矩阵T.的逆矩阵一般不再是Toeplitz矩阵.1972年Gohberg和Semencul给出了一个名结果:如果将Toeplirz矩阵T。  相似文献   

10.
本文主要研究矩阵的非奇异性判别,推广了Szulc[1]和李[2]最近在孩领域所取得的主要结果。  相似文献   

11.
12.
In this paper we discuss the problem whether and how the inverse of a Toeplitz matrix can be recovered from some of its columns or parts of columns under the requirement that only 2n−1 parameters are involved. The results generalize and strengthen earlier findings by Trench, Gohberg, Semencul, Krupnik, Ben-Artzi, Shalom, Labahn, Rodman and others. Special attention is paid to symmetric, skewsymmetric and hermitian Toeplitz matrix inverses and the question whether such a matrix can be retrieved from a single column.  相似文献   

13.
In this paper, we propose a new mean value algorithm for the Toeplitz matrix completion based on the singular value thresholding (SVT) algorithm. The completion matrices generated by the new algorithm keep a feasible Toeplitz structure. Meanwhile, we prove the convergence of the new algorithm under some reasonal conditions. Finally, we show the new algorithm is much more effective than the ALM (augmented Lagrange multiplier) algorithm through numerical experiments and image inpainting.  相似文献   

14.
In this paper, tridiagonal Toeplitz matrix (type I, type II) with opposite-bordered rows are introduced. Main attention is paid to calculate the determinants, the inverses and the eigenpairs of these matrices. Specifically, the determinants of an $n\times n$ tridiagonal Toeplitz matrix with opposite-bordered rows can be explicitly expressed by using the $(n-1)$th Fibonacci number, the inversion of the tridiagonal Toeplitz matrix with opposite-bordered rows can also be explicitly expressed by using the Fibonacci numbers and unknown entries from the new matrix. Besides, we give the expression of eigenvalues and eigenvectors of the tridiagonal Toeplitz matrix with opposite-bordered rows. In addition, some algorithms are presented based on these theoretical results. Numerical results show that the new algorithms have much better computing efficiency than some existing algorithms studied recently.  相似文献   

15.
Let a, b and c be fixed complex numbers. Let M n (a, b, c) be the n × n Toeplitz matrix all of whose entries above the diagonal are a, all of whose entries below the diagonal are b, and all of whose entries on the diagonal are c. For 1 ⩽ kn, each k × k principal minor of M n (a, b, c) has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of M n (a, b, c). We also show that all complex polynomials in M n (a, b, c) are Toeplitz matrices. In particular, the inverse of M n (a, b, c) is a Toeplitz matrix when it exists.  相似文献   

16.
关于Toeplitz矩阵的某些注记   总被引:1,自引:0,他引:1  
In this paper,we study real symmetric Toeplitz matrices commutable with tridi-agonal matrices, present more detailed results than those in [1], and extend them to non-symmetric Toeplitz matrices. Also, complex Toeplitz matrices, especially the corresponding matrices of lower order, are discussed.  相似文献   

17.
An n × n complex matrix A is said to be k-potent if A k = A. Let T 1 and T 2 be k-potent and c 1 and c 2 be two nonzero complex numbers. We study the range space, null space, nonsingularity and group invertibility of linear combinations T = c 1 T 1 + c 2 T 2 of two k-potent matrices T 1 and T 2.  相似文献   

18.
Given an n × n matrix F, we find the nearest symmetric positive semi‐definite Toeplitz matrix T to F. The problem is formulated as a non‐linear minimization problem with positive semi‐definite Toeplitz matrix as constraints. Then a computational framework is given. An algorithm with rapid convergence is obtained by l1 Sequential Quadratic Programming (SQP) method. Copyright © 2002 John Wiley & Sons, Ltd.  相似文献   

19.
20.
We study the asymptotic behaviour of the eigenvalues of Hermitian block Toeplitz matrices , with Toeplitz blocks. Such matrices are generated by the Fourier coefficients of an integrable bivariate function , and we study their eigenvalues for large and , relating their behaviour to some properties of as a function; in particular we show that, for any fixed , the first eigenvalues of tend to , while the last tend to , so extending to the block case a well-known result due to Szegö. In the case the 's are positive-definite, we study the asymptotic spectrum of , where is a block Toeplitz preconditioner for the conjugate gradient method, applied to solve the system , obtaining strict estimates, when and are fixed, and exact limit values, when and tend to infinity, for both the condition number and the conjugate gradient convergence factor of the previous matrices. Extensions to the case of a deeper nesting level of the block structure are also discussed.

  相似文献   


设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号