Accession Number : AD0675976

Title :   ON THE SIMPLIFICATION OF THE LINEAR APPROXIMATION PROBLEM IN HILBERT SPACE WITH APPLICATIONS TO LEAST SQUARES,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Blum,Marvin

Report Date : SEP 1968

Pagination or Media Count : 23

Abstract : A method for reducing the order of a matrix inversion required in the linear approximation problem in Hilbert space has been derived. The method depends on identifying the components of the basis vectors of the approximating vectors with the members of an orthonormal sequence in the Hilbert space. The method has been applied to a number of examples in L superscript 2(a,b) to show how the least squares solution may be simplified by reducing the order of matrix inversion required. The main results of the paper are presented for the reduced solution in abstract Hilbert space. The specific form of the general equations has been applied to three examples in the Hilbert space L superscript 2(a,b) a,b finite. (Author)

Descriptors :   (*APPROXIMATION(MATHEMATICS), HILBERT SPACE), (*LEAST SQUARES METHOD, APPROXIMATION(MATHEMATICS)), FUNCTIONAL ANALYSIS, MATRICES(MATHEMATICS), MEASURE THEORY, OPTIMIZATION

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE