A look-ahead Lánczos algorithm for unsymmetric matrices
نویسندگان
چکیده
منابع مشابه
A Look-ahead Bareiss Algorithm for General Toeplitz Matrices
The Bareiss algorithm is one of the classical fast solvers for systems of linear equations with Toeplitz coeecient matrices. The method takes advantage of the special structure, and it computes the solution of a Toeplitz system of order N with only O(N 2) arithmetic operations, instead of O(N 3) operations. However, the original Bareiss algorithm requires that all leading principal sub-matrices...
متن کاملA look-ahead Schur Algorithm
The classical Schur algorithm computes the LDL T factorization of a symmetric Toeplitz matrix in O(n 2) operations, but requires that all the principal minors of the matrix be nonsingular. Look-ahead schemes have been proposed to deal with matrices that have exactly singular principal minors 9], 11]. Unfortunately, these algorithms cannot be extended to matrices that have ill-conditioned princi...
متن کاملA Block Toeplitz Look-ahead Schur Algorithm
This paper gives a look-ahead Schur algorithm for nding the symmetric factorization of a Hermitian block Toeplitz matrix. The method is based on matrix operations and does not require any relations with orthogonal polynomials. The simplicity of the matrix based approach ought to shed new light on other issues such as parallelism and numerical stability.
متن کاملAn Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices
The nonsymmetric Lanczos method can be used to compute eigenvalues of large sparse non-Hermitian matrices or to solve large sparse non-Hermitian linear systems. However, the original Lanczos algorithm is susceptible to possible breakdowns and potential instabilities. We present an implementation of a look-ahead version of the Lanczos algorithm that|except for the very special situation of an in...
متن کاملAn Implementation of the Look-Ahead Lanczos Algorithm for Non-Hermitian Matrices Part II
In Part I [6] of this paper, we have presented an implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices. Here, we show how the look-ahead Lanczos process | combined with a quasi-minimal residual (QMR) approach | can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are p...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1985
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1985-0771034-2