Optimal secant-updates of rank 1

• Autores: A. Galperin
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 253, Nº 1, 2013, págs. 66-79
• Idioma: inglés
• DOI: 10.1016/j.cam.2013.04.001
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• Resumen

  • 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.