Accession Number : AD0703663

Title :   MATHEMATICAL PROGRAMMING AND THE NUMERICAL SOLUTION OF LINEAR EQUATIONS.

Descriptive Note : Final rept.,

Corporate Author : TENNECOMP INC OAK RIDGE TENN

Personal Author(s) : Rust,Bert W. ; Burrus,Walter R.

Report Date : MAR 1970

Pagination or Media Count : 335

Abstract : The book is concerned with the use of mathematical programming techniques for solving ill-conditioned systems of linear equations with various kinds of errors in the right hand side vector. The primary motivation for the work was the spectrum unfolding problem of experimental physics, so the treatment also includes the Fredholm integral equation of the first kind, which can be considered to be an infinite dimensional ill-conditioned system. The basic idea of the new techniques which are developed is the use of priori knowledge about the solution in order to greatly reduce the size of the class of solutions which are consistent with the right hand side errors. The methods are designed to give interval estimates for the solution--the sizes of the intervals being determined by the sizes of the errors in the right hand side, and the constraints imposed on the class of acceptable solutions by the a priori information. The basic a priori constraint which is used is that the solution must be non-negative; but it is shown that many other a priori constraints can be reduced to a simple non-negativity constraint by a suitable transformation of variables. When the non-negativity constraint is taken into account, the problem of estimating lower and upper bounds for the solution can be formulated and solved as a mathematical programming problem. The book treats both the case where the right hand side errors are known absolutely to lie in some bounded region and also the case where the errors are normally distributed. (Author)

Descriptors :   (*MATHEMATICAL PROGRAMMING, LINEAR SYSTEMS), (*INTEGRAL EQUATIONS, NUMERICAL ANALYSIS), FUNCTIONAL ANALYSIS, MATRICES(MATHEMATICS), REGRESSION ANALYSIS, MATHEMATICAL PREDICTION, CONFIDENCE LIMITS, UNCERTAINTY, PROBABILITY DENSITY FUNCTIONS, QUADRATIC PROGRAMMING, LINEAR PROGRAMMING, SIMPLEX METHOD, ALGORITHMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE