Accession Number : AD0677107

Title :   NORMS AND INEQUALITIES FOR CONDITION NUMBERS, II,

Corporate Author : BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH MATHEMATICS RESEARCH LAB

Personal Author(s) : Marshall,Albert W. ; Olkin,Ingram

Report Date : SEP 1968

Pagination or Media Count : 13

Abstract : The condition number c sub phi of a nonsingular matrix A is defined by c sub phi (A) = phi (A) phi (A superscript -1) where ordinarily phi is a norm. It was shown by J. D. Riley that if A is positive definite, c sub phi (A + kI) = or < c sub phi (A) when k > 0 and phi squared (A) is the maximum eigenvalue of AA* or phi squared (A) = Tr AA*. In this paper it is shown more generally that c sub phi (A + B) = or < c sub phi (B) when phi satisfies phi (U) = or < phi (V) if V-U is positive definite and when A,B are positive definite satisfying c sub phi (A) = or < c sub phi (B). Some related inequalities are also obtained. As suggested by Riley, these results may be of practical use in solving a system Ax = d of linear equations when A is positive definite but ill-conditioned. (Author)

Descriptors :   (*MATRICES(MATHEMATICS), INEQUALITIES), INVARIANCE, VECTOR SPACES, THEOREMS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE