Linear-System Solver for EFG-Type Saddle-Point Problem without Using QR Decomposition

Abstract

A novel method is proposed for solving an EFG-type Saddle-Point (EFG-SP) problem. Although the null-space method and the variable-reduction method (VRM) were developed as a solver of a saddle-point problem, both methods are extremely time-consuming in solving an EFG-SP problem. This is attributable to the QR decomposition that is indispensable for both methods. For the purpose of resolving this problem, the improved Variable-Reduction Method (iVRM) is formulated without using the QR decomposition. A numerical code has been developed for solving an EFG-SP problem with the iVRM, the VRM and the ICCG method. By means of the code, the performance of the three methods is investigated numerically. The results of computations show that, from the standpoint of convergence property and computational speed, the iVRM is even superior to either of the VRM and the ICCG method.