Error-free computer solution of certain systems of linear equations

Stephen F. Chang, William J. Kennedy
1987 Journal of Computational and Applied Mathematics  
In this article we propose a procedure which generates the exact solution for the system Ax = b, where A is an integral nonsingular matrix and b is an integral vector, by improving the initial floating-point approximation to the solution. This procedure, based on an easily programmed method proposed by Aberth [l], first computes the approximate floating-point solution x * by using an available linear equation solving algorithm. Then it extracts the exact solution x from x* if the error in the
more » ... proximation x * is sufficiently small. An a posteriori upper bound for the error of x * is derived when Gaussian Elimination with partial pivoting is used. Also, a computable upper bound for ]det(A) 1, which is an alternative to using Hadamard's inequality, is obtained as a byproduct of the Gaussian Elimination process.
doi:10.1016/0377-0427(87)90002-1 fatcat:c2236bfa75dtzfayf2ltkobuku