On twisted factorizations of block tridiagonal matrices
نویسندگان
چکیده
Non-symmetric and symmetric twisted block factorizations of block tridiagonal matrices are discussed. In contrast to non-blocked factorizations of this type, localized pivoting strategies can be integrated which improves numerical stability without causing any extra fill-in. Moreover, the application of such factorizations for approximating an eigenvector of a block tridiagonal matrix, given an approximation of the corresponding eigenvalue, is outlined. A heuristic strategy for determining a suitable starting vector for the underlying inverse iteration process is proposed.
منابع مشابه
“Computation of Eigenvectors of Block Tridiagonal Matrices Based on Twisted Factorizations” Verfasser
Computing the eigenvalues and eigenvectors of a band or block tridiagonal matrix is an important aspect of various applications in Scientific Computing. Most existing algorithms for computing eigenvectors of a band matrix rely on a prior tridiagonalization of the matrix. While the eigenvalues and eigenvectors of tridiagonal matrices can be computed very efficiently, the preceding tridiagonaliza...
متن کاملStable Factorizations of Symmetric Tridiagonal and Triadic Matrices
We call a matrix triadic if it has no more than two nonzero off-diagonal elements in any column. A symmetric tridiagonal matrix is a special case. In this paper we consider LXLT factorizations of symmetric triadic matrices, where L is unit lower triangular and X is diagonal, block diagonal with 1×1 and 2×2 blocks, or the identity with L lower triangular. We prove that with diagonal pivoting, th...
متن کاملOn the nonnegative inverse eigenvalue problem of traditional matrices
In this paper, at first for a given set of real or complex numbers $sigma$ with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which $sigma$ is its spectrum. In continue we present some conditions for existence such nonnegative tridiagonal matrices.
متن کاملBLU Factorization for Block Tridiagonal Matrices and Its Error Analysis
A block representation of the BLU factorization for block tridiagonal matrices is presented. Some properties on the factors obtained in the course of the factorization are studied. Simpler expressions for errors incurred at the process of the factorization for block tridiagonal matrices are considered.
متن کاملEigendecomposition of Block Tridiagonal Matrices
Block tridiagonal matrices arise in applied mathematics, physics, and signal processing. Many applications require knowledge of eigenvalues and eigenvectors of block tridiagonal matrices, which can be prohibitively expensive for large matrix sizes. In this paper, we address the problem of the eigendecomposition of block tridiagonal matrices by studying a connection between their eigenvalues and...
متن کامل