Matrix splitting principles
The author discusses the solution of systems of linear equations \(Ax = b\) by means of iterative methods based on matrix splittings \(A = M - N\) with a nonsingular matrix \(M\). The author gives a definition of a regular, nonnegative, weak nonnegative, weak, weaker and convergent splitting of \(A\). A systematic analysis of convergence conditions used in comparison theorems is presented. A scheme of condition implications for regular splittings of \(A = M_1 - N_1 = M_2 - N_2\), where \(A^{-1} \geq 0\), is given. Furthermore, nonnegative and weak nonnegative splittings as well as weak and weaker splittings are analysed in detail.
scientific article; zbMATH DE number 1780266