MATRIX MANIPULATIONS BY COMPUTER: COMPUTATION OF FUNCTIONS OF A MATRIX.
SYSTEM DEVELOPMENT CORP SANTA MONICA CALIF
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A program is described for the calculation of functions of numeric matrices. The methods of Krylov and Leverrier are used. The program presented calculates the characteristic equation of the matrix by Krylovs method, then obtains the eigenvalues by finding the roots of this equation. In the enclosed program the method of Muller is used, although any other root-solving routine would work also. Calculations for complex eigenvalues are terminated, since the required complex arithmetic is quite unwieldy and is not included in this program. Such calculations could easily be carried out in FORTRAN IV. For real eigenvalues the function is calculated using the Cayley-Hamilton Theorem for finding the coefficients of the finite expansion of the function in powers of the given matrix. Repeated eigenvalues are also handled by this program, although the resultant numerical accuracy is not very good. The program is not optimized in any way it is intended for teaching purposes and therefore prints copious intermediate results. A FORTRAN II program, checked on a Philco 2000 ALTAC III compiler, is given here. Author
- Theoretical Mathematics
- Computer Programming and Software