Resumen de Optimal secant-updates of rank 1

A. Galperin

• Weconsider a class of secant update iterative methods for solving nonlinear operator equations in Hilbert spaces. Our goal is to characterize optimal inverse secant-updates of rank 1. As the optimality criterion we use the factor, by which one iteration of a secant update iterative method reduces the entropy of solution�s position within the set of its guaranteed existence and uniqueness. Having got the optimality condition, we select among optimal updates of rank 1 one that minimizes the condition number of the updated operator. The resulting update determines a new secant update iterative method.