SOLVING SYSTEMS OF LINEAR EQUATIONS BY USING THE GENERALIZED INVERSE.
Abstract
The report proves that a particular vector function, defined on real n-space, is a least squares solution for any real m x n linear system of equations (Ax = b). Expressed in terms of the coefficient matrix A, the generalized inverse A prime of matrix A, and the vector b, the function is shown to be the complete solution of the system provided that a solution exists. The particular functional element A prime b of smallest Euclidean length is discussed with regard to its applications in solving systems of linear and nonlinear equations, in curve fitting, and in finding least squares estimates of linear regression coefficients. A program that computes A prime is described briefly. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 04, 1968
- Accession Number
- AD0667727
Entities
People
- Marvin J. Goldstein
Organizations
- Navy Underwater Sound Laboratory