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Special Criteria for Inverse Stability

  • H.-J. Reinhardt
Chapter
Part of the Applied Mathematical Sciences book series (AMS, volume 57)

Abstract

In this chapter, we analyze special criteria which guarantee for linear problems the inverse stability inequalities established in Chapter 11. These criteria strongly depend on the norms of the approximating spaces. The significance of the choice of norms was already made clear in Section 11.1 where we verified the differentiability requirements for several classes of examples. The analysis in this chapter, moreover, is applicable to nonlinear problems. Indeed, we know that the inverse stability of a nonlinear sequence of differentiable mappings is guaranteed whenever the associated sequence of Fréchet-derivatives is inversely stable.

Keywords

Galerkin Method Special Criterion Explicit Method Uniform Boundedness Supremum Norm 
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References (cf. also References in Chapters 4 and 11)

  1. Ciarlet (1978), Fairweather (1978), Forsythe & Wasow (1967), Meis & Marcowitz (1981), Richtmyer & Morton (1967), Törnig (1979), Törnig & Ziegler (1966)*, Varga (1962).Google Scholar

Copyright information

© Springer Science+Business Media New York 1985

Authors and Affiliations

  • H.-J. Reinhardt
    • 1
  1. 1.Fachbereich MathematikJohann-Wolfgang-Goethe-Universität6000 Frankfurt MainFederal Republic of Germany

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