DECAY BOUNDS AND O(n) ALGORITHMS FOR APPROXIMATING FUNCTIONS OF SPARSE MATRICES

被引：0

作者：

Benzi, Michele ^{[1
]}

Razouk, Nader ^{[1
]}

机构：

[1] Emory Univ, Dept Math & Comp Sci, Atlanta, GA 30322 USA

来源：

ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS | 2007年 / 28卷

基金：

美国国家科学基金会;

关键词：

Matrix functions; sparse and banded matrices; decay rates; linear time algorithms; Chebyshev polynomials; Faber polynomials; density matrix; trace; determinant; ELECTRONIC-STRUCTURE CALCULATIONS; KRYLOV SUBSPACE APPROXIMATIONS; DENSITY-MATRIX; EXPONENTIAL OPERATOR; COMPUTATION; INVERSE; DIFFUSION; SYSTEMS; RATES;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We establish decay bounds for the entries of f(A), where A is a sparse (in particular, banded) n x n diagonalizable matrix and f is smooth on a subset of the complex plane containing the spectrum of A. Combined with techniques from approximation theory, the bounds are used to compute sparse (or banded) approximations to f(A), resulting in algorithms that under appropriate conditions have linear complexity in the matrix dimension. Applications to various types of problems are discussed and illustrated by numerical examples.

引用

页码：16 / 39

页数：24

共 81 条

[1] ABSENCE OF DIFFUSION IN CERTAIN RANDOM LATTICES [J].