The Role of the Strengthened Cauchy-Buniakowskii-Schwarz Inequality in Multilevel Methods

The basic theory of the strengthened Cauchy-Buniakowskii-Schwarz inequality and its applications in multilevel methods for the solution of linear systems arising from finite element or finite difference discretisation of elliptic partial differential equations is surveyed. Proofs are given both in a...

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Bibliographic Details
Published in:SIAM review 1991-09, Vol.33 (3), p.405-419
Main Authors: Eijkhout, Victor, Vassilevski, Panayot
Format: Article
Language:English
Subjects:
Algebra
Applied mathematics
Cauchy Schwarz inequality
Eigenvalues
Exact sciences and technology
Iterative methods
Mathematical vectors
Mathematics
Matrices
Multigrid methods
Numerical analysis
Numerical analysis. Scientific computation
Partial differential equations
Partial differential equations, boundary value problems
Polynomials
Sciences and techniques of general use
Stiffness matrix
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Summary:The basic theory of the strengthened Cauchy-Buniakowskii-Schwarz inequality and its applications in multilevel methods for the solution of linear systems arising from finite element or finite difference discretisation of elliptic partial differential equations is surveyed. Proofs are given both in a finite element context, and in purely algebraic form.
ISSN:0036-1445
1095-7200
DOI:10.1137/1033098