Consider the linear system Ax=b where the coefficient matrix A is an M-matrix. In the present work, it is proved that the rate of convergence of the Gauss-Seidel method is faster than the mixed-type splitting and AOR (SOR) iterative methods for solving M-matrix linear systems. Furthermore, we improve the rate of convergence of the mixed-type splitting iterative method by applying a preconditio...

The smoothness-constrained least-squares method is widely used for two-dimensional (2D) and three-dimensional (3D) inversion of apparent resistivity data sets. The Gauss–Newton method that recalculates the Jacobian matrix of partial derivatives for all iterations is commonly used to solve the least-squares equation. The quasi-Newton method has also been used to reduce the computer time. In this...

In this paper, a Gauss–Seidel method with oblique direction (GSO) is proposed for finding the least-squares solution to system of linear equations, where coefficient matrix may be full rank or deficient and overdetermined underdetermined. Through method, number iteration steps running time can reduced greater extent find solution, especially when columns A are close correlation. It theoreticall...

Solving a set of simultaneous linear equations is probably the most important topic in numerical methods. For solving linear equations, iterative methods are preferred over the direct methods specially when the coefficient matrix is sparse. The rate of convergence of iteration method is increased by using Successive Relaxation (SR) technique. But SR technique is very much sensitive to relaxatio...

The post-optimality analysis of a tetrahedral formation flying optimal control problem is considered. In particular, this four-spacecraft orbit insertion problem is transcribed to a nonlinear programming problem (NLP) using a direct method called the Gauss pseudospectral method. The Karush-Kuhn-Tucker (KKT) conditions for this NLP are then derived and are compared to the conditions obtained via...