The continued fraction methods for the solution of systems of linear equations
A class of iterative methods for the computation of a minimal residual norm solution of a system of linear equations \(Ax=b\) is presented, where A is a rectangular matrix. Special cases of the method, i.e. special choices of the inner product and the search vectors used, include the classical conjugate gradient method and the modified conjugate gradient method minimizing the residual. A test example for the Laplacian model problem shows that the flexibility about the number and the direction of search vectors may result in better convergence properties.
scientific article; zbMATH DE number 3854306