PROCESSING OF LINEAR SYSTEMS OF EQUATIONS

A method for processing linear systems of equations and finding a nx1 vector x satisfying Ax=b where A is a symmetric, positive-definite nxn matrix corresponding to nxn predefined high-precision elements and b is an n1 vector corresponding to n predefined high-precision elements. A first iterative process generates n low-precision elements corresponding to an nx1 vector x1 satisfying A1x1=b1 where A1, b1 are elements in low precision. The elements are converted to high-precision data elements to obtain a current solution vector x. A second iterative process generates n low-precision data elements corresponding to an nx1 correction vector dependent on the difference between the vector b and the vector product Ax. Then there is produced from the n low-precision data elements of the correction vector respective high-precision data elements of an nx1 update vector u. The data elements of the current solution vector x are updated such that x=x±u.