Polynominal Approximation of Functions of Matrices and Its Application the the Solution of a General System of Linear Equations
Abstract
Frequently, during the process of solving a mathematical model numerically, we end up with a need to operate on a vector v by an operator which can be expressed as f (A) while A is N x N matrix. Except for very simple matrices, it is impractical to construct the matrix f(A) explicity. Usually an approximation to it is used. In the present research, we develop an algorithm which uses a polynomial approximation to f(A). It is reduced to a problem of approximating f(z) by a polynomial in z while z belongs to the domain D in the complex plane which includes all the eigenvalues of A. This problem of approximation is approached by interpolating the function f (z) in a certain set of points which is known to have some maximal properties. The approximation thus achieved is almost best. Implementing the algorithm to some practical problem is described.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 31, 1987
- Accession Number
- ADA211390
Entities
People
- Hillel Tal-ezer