USING CONJUGATE GRADIENTS PROJECTION METHOD FOR SOLVING ILL-POSED PROBLEMS ON THE SPECIAL SETS

Abstract

The paper deals with numerical methods for the solution of ill-posed problems on special sets. A definition of well-posed problem is given. A conjugate gradients projection method and a program written in the programming language Matlab, which solve the problem on 28 special sets of correctness are briefly described. Some results for the numerical solution of Fredholm’s integral equation of the first kind are presented. The method for solving systems of linear algebraic equations on special sets has been used also for the functions smoothing for the experimental measurement data.

Keywords

• systems of linear algebraic equations
• special sets
• ill-posed problems
• conjugate gradients projection method
• stabilization methods
• quasisolution
• Fredholm’s integral equation of the first kind