Optimally conditioned scaled ABS algorithms for linear systems
Using a strict bound of the first author to the condition number of bordered positive-definite matrices, we show that the scaling parameter in the ABS class for linear systems can always be chosen so that the bound of a certain update matrix is globally minimized. Moreover, if the scaling parameter is so chosen at every iteration, then the condition number itself is globally minimized. The resulting class of optimally conditioned algorithms contains as a special case the class of optimally stable algorithms in the sense of Broyden.
scientific article; zbMATH DE number 4128298