نتایج جستجو برای: tridiagonal matrix

تعداد نتایج: 365390  

Journal: :Applied Mathematics and Computation 2011
Boris Igelnik Dan Simon

We derive the eigenvalues of a tridiagonal matrix with a special structure. A conjecture about the eigenvalues was presented in a previous paper, and here we prove the conjecture. The matrix structure that we consider has applications in biogeography theory. 2011 Elsevier Inc. All rights reserved. 1. Main result and related work We prove the following theorem in this paper. Theorem 1. The (n + ...

Journal: :SIAM J. Matrix Analysis Applications 2009
Beresford N. Parlett Christof Vömel

In this paper, we analyze the distribution of the eigenvalues of glued tridiagonal matrices. Such matrices provide a useful class of test matrix because, despite being unreduced, a glued matrix can have some eigenvalues agreeing to hundreds of decimal places. A glued matrix can be obtained from a direct sum of p copies of an unreduced symmetric tridiagonal matrix T by modifying the junctions, i...

Journal: :Digital Signal Processing 2012
Magdy T. Hanna

a Nearly Tridiagonal Matrix Magdy Tawfik Hanna1 ABSTRACT A fully-fledged definition for the fractional discrete Fourier transform of type IV (FDFT-IV) is presented and shown to outperform the simple definition of the FDFT-IV which is proved to be just a linear combination of the signal, its DFT-IV and their flipped versions. This definition heavily depends on the availability of orthonormal eig...

Journal: :SIAM J. Matrix Analysis Applications 2005
Marc Van Barel Raf Vandebril Nicola Mastronardi

An orthogonal similarity reduction of a matrix to semiseparable form. Abstract It is well known how any symmetric matrix can be reduced by an orthogonal similarity transformation into tridiagonal form. Once the tridiagonal matrix has been computed, several algorithms can be used to compute either the whole spectrum or part of it. In this paper, we propose an algorithm to reduce any symmetric ma...

2010
PIERLUIGI AMODIO

Tridiagonal systems play a fundamental role in matrix computation. In particular, in recent years parallel algorithms for the solution of tridiagonal systems have been developed. Among these, the cyclic reduction algorithm is particularly interesting. Here the stability of the cyclic reduction method is studied under the assumption of diagonal dominance. A backward error analysis is made, yield...

Journal: :SIAM J. Scientific Computing 2011
Sou-Cheng T. Choi Christopher C. Paige Michael A. Saunders

CG, SYMMLQ, and MINRES are Krylóv subspace methods for solving symmetric systems of linear equations. When these methods are applied to an incompatible system (that is, a singular symmetric least-squares problem), CG could break down and SYMMLQ’s solution could explode, while MINRES would give a least-squares solution but not necessarily the minimum-length (pseudoinverse) solution. This underst...

2006
Masami Takata Taro Konda Kinji Kimura Yoshimasa Nakamura

Let a singular value of a bidiagonal matrix be known. Then the corresponding singular vector can be computed through the twisted factorization of a tridiagonal matrix by the discrete Lotka-Volterra with variable step-size (dLVv) transformation. Errors of the singular value then sensitively affect the conditional number of the tridiagonal matrix. In this paper, we first examine a relationship be...

Journal: :CoRR 2012
Lajos László

Abstract. We find the minimum scale factor, for which the nonnegative Böttcher-Wenzel biquadratic form becomes a sum of squares (sos). To this we give the primal and dual solutions for the underlying semidefinite program. Moreover, for special matrix classes (tridiagonal, backward tridiagonal and cyclic Hankel matrices) we show that the above form is sos. Finally, we conjecture sos representabi...

Journal: :Oper. Res. Lett. 2012
Bernd Gärtner Markus Sprecher

We give a polynomial-time dynamic programming algorithm for solving the linear complementarity problem with tridiagonal or, more generally, Hessenberg P-matrices. We briefly review three known tractable matrix classes and show that none of them contains all tridiagonal P-matrices.

2015
Faiz Atlan Moawwad El-Mikkawy F. Atlan M. El-Mikkawy

In the current article we propose a new efficient, reliable and breakdown-free algorithm for solving general opposite-bordered tridiagonal linear systems. An explicit formula for computing the determinant of an opposite-bordered tridiagonal matrix is investigated. Some illustrative examples are given.

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