Revisiting (k , l)-step methods
نویسندگان
چکیده
Abstract. In the mid-1980s B.N. Parsons [29] and the author [10] independently had the idea to generalize linear stationary k-step methods to stationary (k, l)-step methods, which were further generalized to nonstationary and even nonlinear (k, l)-step methods. Later, conjugate-gradient-type methods that are (k, l)-step methods of a similar sort were introduced and investigated in the PhD thesis of Teri Barth [3]. Recently, the family of Induced Dimension Reduction (IDR) methods [32] aroused some interest for the class of linear nonstationary (k, l)-step methods because IDR(s) fits into it and belongs to a somewhat special subclass [14]. In this paper we first reformulate and review the class of linear nonstationary (k, l)-step methods and a basic theoretical result obtained in [10]. Then we introduce alternative iterations that can be used to implement them and compare them with the iterations suggested and investigated by Barth.
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