期刊
BIT NUMERICAL MATHEMATICS
卷 56, 期 3, 页码 1045-1067出版社
SPRINGER
DOI: 10.1007/s10543-015-0592-7
关键词
Matrix functional; Gauss quadrature; Averaged Gauss rules
资金
- Serbian Ministry of Education, Science and Technological Development Methods of numerical and nonlinear analysis with applications [174002]
- NSF [DMS-1115385]
The need to compute expressions of the form , where A is a large square matrix, u and v are vectors, and f is a function, arises in many applications, including network analysis, quantum chromodynamics, and the solution of linear discrete ill-posed problems. Commonly used approaches first reduce A to a small matrix by a few steps of the Hermitian or non-Hermitian Lanczos processes and then evaluate the reduced problem. This paper describes a new method to determine error estimates for computed quantities and shows how to achieve higher accuracy than available methods for essentially the same computational effort. Our methods are based on recently proposed generalized averaged Gauss quadrature formulas.
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