SOLVING SYSTEMS OF LINEAR EQUATIONS BY USING THE GENERALIZED INVERSE.
NAVY UNDERWATER SOUND LAB NEW LONDON CONN
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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
- Statistics and Probability