PDF] Steepest Descent and Conjugate Gradient Methods with Variable Preconditioning
Por um escritor misterioso
Last updated 24 outubro 2024
It is shown that the CG method with variable preconditioning under this assumption may not give improvement, compared to the steepest descent (SD) method, and a new elegant geometric proof of the SD convergence rate bound is given. We analyze the conjugate gradient (CG) method with variable preconditioning for solving a linear system with a real symmetric positive definite (SPD) matrix of coefficients $A$. We assume that the preconditioner is SPD on each step, and that the condition number of the preconditioned system matrix is bounded above by a constant independent of the step number. We show that the CG method with variable preconditioning under this assumption may not give improvement, compared to the steepest descent (SD) method. We describe the basic theory of CG methods with variable preconditioning with the emphasis on “worst case” scenarios, and provide complete proofs of all facts not available in the literature. We give a new elegant geometric proof of the SD convergence rate bound. Our numerical experiments, comparing the preconditioned SD and CG methods, not only support and illustrate our theoretical findings, but also reveal two surprising and potentially practically important effects. First, we analyze variable preconditioning in the form of inner-outer iterations. In previous such tests, the unpreconditioned CG inner iterations are applied to an artificial system with some fixed preconditioner as a matrix of coefficients. We test a different scenario, where the unpreconditioned CG inner iterations solve linear systems with the original system matrix $A$. We demonstrate that the CG-SD inner-outer iterations perform as well as the CG-CG inner-outer iterations in these tests. Second, we compare the CG methods using a two-grid preconditioning with fixed and randomly chosen coarse grids, and observe that the fixed preconditioner method is twice as slow as the method with random preconditioning.
The Conjugate Gradient Method
Steepest Descent Methods
Preconditioned conjugate gradient method for finding minimal
Descent carefully on a gradient!. In machine learning, gradient
PDF] Steepest Descent and Conjugate Gradient Methods with Variable
A Descent Four-Term Conjugate Gradient Method with Global
Conjugate gradient method - Wikipedia
4.2 - 1b - Gradient Descent - Wikipedia - Workedout
PDF] An Introduction to the Conjugate Gradient Method Without the
Gradient descent - Wikipedia
Conjugate gradient method - Wikipedia
PDF) Comparison Between Steepest Descent Method and Conjugate
Recomendado para você
-
Method of steepest descent - Wikipedia24 outubro 2024
-
Steepest Descent Method24 outubro 2024
-
Gradient descent - Wikipedia24 outubro 2024
-
Steepest Descent Method - an overview24 outubro 2024
-
PPT - 4. Method of Steepest Descent PowerPoint Presentation, free download - ID:565484524 outubro 2024
-
Gradient Descent Algorithm in Machine Learning - Analytics Vidhya24 outubro 2024
-
MATLAB script file implementing the method of steepest descent24 outubro 2024
-
nonlinear optimization - Do we need steepest descent methods, when minimizing quadratic functions? - Mathematics Stack Exchange24 outubro 2024
-
Solved The steepest descent method for minimize f(x) is the24 outubro 2024
-
Steepest Descent - an overview24 outubro 2024
você pode gostar
-
Anais do II Congresso Internacional de Pesquisa em Literatura e XIV Seminário de Estudos Literários by HN Editora Publieditorial - Issuu24 outubro 2024
-
Open book vector clipart set, symbol, icon design. Illustration isolated on white background Stock Vector Image & Art - Alamy24 outubro 2024
-
Com dois de Pedro, Flamengo bate o Palmeiras no Maracanã e entra de vez na briga pelo título do Brasileirão24 outubro 2024
-
Bom dia para Whatsapp 2023: 100 Imagens com mensagens24 outubro 2024
-
Gift Card (For Meal Prep Purchases Only) — Evenroods24 outubro 2024
-
ALL ABOUT ASIAN DRAMA: Review on Japanese Drama: Buzzer Beat (2009)24 outubro 2024
-
hyakuren no valkyria episode 2 (Sub Indo) - BiliBili24 outubro 2024
-
Jogo Pokémon - Coleção Premium - Umbreon-GX - Copag - Ri Happy24 outubro 2024
-
Resident Evil Code: Veronica X - SteamGridDB24 outubro 2024
-
Pokemon Go Gen 5 Pokemon arrive today – Here's what you can catch, and when - Daily Star24 outubro 2024