On Some Inverse Singular Value Problems with Toeplitz-Related Structure
نویسندگان
چکیده
In this paper, we consider some inverse singular value problems for Toeplitz-related matrices. We construct a Toeplitz-plus-Hankel matrix from prescribed singular values including a zero singular value. Then we find a solution to the inverse singular value problem for Toeplitz matrices which have double singular values including a double zero singular value.
منابع مشابه
Sequential and Parallel Algorithms for the Inverse Toeplitz Singular Value Problem
When the Inverse Additive Singular Value Problem (IASVP) involves Toeplitz–type matrices it is possible to exploit this special structure to reduce the execution time. In this paper, we present two iterative local and global convergent algorithms (MIIIT and LPT) to solve efficiently the IASVP when the matrix is Toeplitz (IASVPT). As it will be shown, it can be achieved an asymptotic complexity ...
متن کاملMean value theorem for integrals and its application on numerically solving of Fredholm integral equation of second kind with Toeplitz plus Hankel Kernel
The subject of this paper is the solution of the Fredholm integral equation with Toeplitz, Hankel and the Toeplitz plus Hankel kernel. The mean value theorem for integrals is applied and then extended for solving high dimensional problems and finally, some example and graph of error function are presented to show the ability and simplicity of the method.
متن کاملOn group inverse of singular Toeplitz matrices
In this paper we show that the group inverse of a real singular Toeplitz matrix can be represented as the sum of products of lower and upper triangular Toeplitz matrices. Such a matrix representation generalizes “Gohberg–Semencul formula” in the literature. © 2004 Elsevier Inc. All rights reserved. AMS classification: 15A09; 65F20
متن کاملOn inverse problem for singular Sturm-Liouville operator with discontinuity conditions
In this study, properties of spectral characteristic are investigated for singular Sturm-Liouville operators in the case where an eigen parameter not only appears in the differential equation but is also linearly contained in the jump conditions. Also Weyl function for considering operator has been defined and the theorems which related to uniqueness of solution of inverse proble...
متن کاملTR-2002002: Can We Optimize Toeplitz/Hankel Computations? II. Singular Toeplitz/Hankel-like Case
In Part I, under the bit operation cost model we achieved nearly optimal randomized solution of nonsingular Toeplitz/Hankel linear system of equations based on Hensel's lifting. In Part II, we extend these results to the singular Toeplitz/Hankel-like case based on the MBA divide-and conquer algorithm and its combination with Hensel's lifting. We specify randomization and estimate the error/fail...
متن کامل