Two alternative methods for computing the matrix cosine

Author

Alan LaMont Fisher

Date of Award

8-1986

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Steven M. Serbin

Committee Members

C. Wagner, O. A. Karakashian

Abstract

We discuss and analyze two methods which may be used to approximate the cosine of a matrix. The two methods are similar in that they both form a rational approximation R(kA) to the matrix cosine, cos(kA), and generate approximate schemes which are based on the exact representation y(t + k) + y(t - k) = 2 cos(kA) y(t) . The methods also allow for our generated approximation to be corrected. The methods differ in that one forms the rational approximation in a partial-fraction form with only linear factors in the denominator, for computational efficiency, especially in a parallel environment. This method allows for the approximation of the local error at any time-step via simple calculations.

The double angle method is presented so that comparisons may be made between it and the time-stepping procedure.

Numerical experiments are performed in order to confirm that our theoretical predictions of convergence rates are valid.

Recommended Citation

Fisher, Alan LaMont, "Two alternative methods for computing the matrix cosine. " Master's Thesis, University of Tennessee, 1986.
https://trace.tennessee.edu/utk_gradthes/13691