ON THE SOLUTION OF LINEAR ALGEBRAIC SYSTEMS BY MATRIX DECOMPOSITION.
HAWAII UNIV HONOLULU
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A theorem is proved which states that the inverse matrix A sup-1sub n of any nonsingular matrix A sub n could be expressed as a unique sequence of U supisub n D supisub n L supisub n products where D supisub n is an n-th order diagonal matrix, U supisub n is a special n-th order upper triangular matrix, L supisub 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 detA sub k not o is also generated in product form. Furthermore the non-zero column above the diagonal of each U supisub n is the solution of the system A subi-1Xsubi-1Csubi0 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
- Theoretical Mathematics