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 finite element context, and in purely algebraic form.

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