IV.—Studies in Practical Mathematics. V. On the Iterative Solution of a System of Linear Equations

Abstract

SynopsisThe convergence of customary processes of iteration for solving linear equations, in particular simple and Seidelian iteration, is studied from the standpoint of matrices. A new variant of Seidelian iteration is introduced. In the positive definite case it always converges, the characteristic roots of its operator being real and positive and less than unity.