{"product_id":"two-level-smoothed-aggregation-methods-aggressive-coarsening-and-massive-polynomial-smoothing-von-radek-tezaur-petr-vanek","title":"Two-level Smoothed Aggregation Methods","description":"\u003cp\u003eThis book, that is based on a scientific material of our works [7, 8, 9, 11], is concerned with an improved convergence analysis of our polynomially accelerated two-level method of [4] and the convergence analysis of its modifications proposed here. The analyzed methods are used for solving linear systems with a positive definite matrix. The methods are based on a smoothed aggregation concept where, in order to make small coarse-space sizes possible, we allow for an aggressive coarsening, that is compensated by massive polynomial smoothing. We show that, for a coarse-space characterized by the diameter of the aggregates H and the fine-level space with the mesh size h, it is sufficient to use O(H\/h) elementary smoothing steps to compensate the dependence of the convergence rate estimate on the coarsening ratio H\/h, and get thereby a convergence rate estimate indepen- dent of the coarse-space size. This feature is not new here; the methods reviewed in [4] belong to this category. In this book, we are interested in a radical improvement of the asymptotic convergence bound with respect to the degree of the smoothing polynomial for certain modifications of the methods presented in [4].\u003c\/p\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9786200487209\"\u003e\u003ch3\u003eAggressive Coarsening and Massive Polynomial Smoothing\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9786200487209","offer_id":39464864219229,"sku":"9786200487209","price":54.9,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/9c301560-ffcd-406f-a6c2-75ff76ca60ae.jpg?v=1773299657","url":"https:\/\/shop.autorenwelt.de\/en\/products\/two-level-smoothed-aggregation-methods-aggressive-coarsening-and-massive-polynomial-smoothing-von-radek-tezaur-petr-vanek","provider":"Autorenwelt Shop","version":"1.0","type":"link"}