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...

This paper deals with the comparative study of preconditioned Symmetric Gauss-Seidel (SGS), New (NSGS), and Parametric (PSGS) methods for solving linear system Ax = b are considered. is precondition type I + S. Convergence properties analyzed standard procedures a numerical experiment undertaken to compare efficiency matrix. Algorithms prepared. MATLAB software used checking computational itera...

In this paper, we consider a self-adaptive extrapolated Gauss-Seidel method for solving the Hermitian positive definite linear systems. Based on optimization models, self-adaptive optimal factor is given. Moreover, we prove the convergence of the self-adaptive extrapolated Gauss-Seidel method without any constraints on optimal factor. Finally, the numerical examples show that the self-adaptive ...

In the paper, we advance a numerical technique for enclosing generalized AE-solution sets to interval linear systems. The main result of the paper is an extension of the well-known interval Gauss-Seidel method to the problems of outer estimation of these generalized solution sets. We give a theoretical study of the new method, prove an optimality property for the generalized interval Gauss-Seid...

Experiments that discuss influence of noise to H. Seidel and H. Herzel dynamics model of human cardiovascular system are presented. Noise is introduced by considering stochastic delays in response to the sympathetic system. It appears that in the presence of the noise 10 s heart rate oscillations connected with Mayer waves are preserved. Moreover the heart rate becomes approximately normally di...

In this paper, the modified Gauss-Seidel method with the new preconditioner for solving the linear system Ax = b, where A is a nonsingular M -matrix with unit diagonal, is considered. The convergence property and the comparison theorems of the proposed method are established. Two examples are given to show the efficiency and effectiveness of the modified Gauss-Seidel method with the presented n...