The Solution of a Quadratic Programming Problem Using Systematic Overrelaxation

Let A be a real symmetric positive definite n n matrix and b a real column n-vector. We consider the following problem: Find real column n-vectors x and y such that \ A x = b + y, \\ xT y = 0, x 0, y 0. \ Problems of this type occur when the method of Christopherson is used to solve free boundary problems for journal bearings. In such cases, A is a “finite difference" matrix. We present a method for solving the above problem which is a modification of systematic over-relaxation. This method is particularly suitable when A is a finite difference matrix.