Accession Number : AD0712680

Title :   ON THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS BY MATRIX DECOMPOSITION.

Descriptive Note : Technical rept.,

Corporate Author : HAWAII UNIV HONOLULU

Personal Author(s) : Tsao,Nai-Kuan ; Kuo,Franklin F.

Report Date : JUL 1970

Pagination or Media Count : 24

Abstract : A theorem is proved which states that the inverse matrix A sup(-1)sub n of any nonsingular matrix A sub n could be expressed as a unique sequence of U sup(i)sub n D sup(i)sub n L sup(i)sub n products where D sup(i)sub n is an n-th order diagonal matrix, U sup(i)sub n is a special n-th order upper triangular matrix, L sup(i)sub n is a special n-th order lower triangular matrix and i runs from 1 up to n. It is also shown that the inverse of each principal minor matrix A sub k with det(A sub k) not = o is also generated in product form. Furthermore the non-zero column above the diagonal of each U sup(i)sub n is the solution of the system A sub(i-1)Xsub(i-1)+Csubi=0 where C sub i = (a sub K,i), 1 < or = k < or = (i-1). The associated algorithm is described together with considerations on storage arrangement, pivoting and operational counts. Finally an example is given in the Appendix. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), LINEAR SYSTEMS, EQUATIONS, PROBLEM SOLVING, NUMERICAL ANALYSIS, ALGORITHMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE