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Strengthened Cauchy–Bunyakowski–Schwarz inequality for a three‐dimensional elasticity system
Author(s) -
Achchab B.,
Axelsson O.,
Laayouni L.,
Souissi A.
Publication year - 2001
Publication title -
numerical linear algebra with applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.02
H-Index - 53
eISSN - 1099-1506
pISSN - 1070-5325
DOI - 10.1002/1099-1506(200104/05)8:3<191::aid-nla229>3.0.co;2-7
Subject(s) - mathematics , elasticity (physics) , cauchy–schwarz inequality , cauchy distribution , rate of convergence , algebraic number , constant (computer programming) , finite element method , iterative method , convergence (economics) , mathematical optimization , inequality , mathematical analysis , computer science , computer network , channel (broadcasting) , materials science , composite material , economics , programming language , economic growth , physics , thermodynamics
The constant γ of the strengthened Cauchy–Bunyakowski–Schwarz (CBS) inequality plays a fundamental role in the convergence rate of multilevel iterative methods. The main purpose of this work is to give an estimate of the constant γ for a three‐dimensional elasticity system. The theoretical results obtained are practically important for the successful implementation of the finite element method to large‐scale modelling of complicated structures as they allow us to construct optimal order algebraic multilevel iterative solvers for a wide class of real‐life elasticity problems. Copyright © 2001 John Wiley & Sons, Ltd.