Stability of spline approximation methods for multidimensional pseudodifferential operators

DOI10.1007/BF01202290zbMath0804.65141OpenAlexW2031409861MaRDI QIDQ1329555

Steffen Roch, R. Hagen, Bernd Silbermann

Publication date: 18 August 1994

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01202290

zbMATH Keywords

stabilitycollocation methodGalerkin methodBanach algebrapseudodifferential operatorssingular integral operatorsFredholm theoryconvolution operatorsclosed manifoldsqualocation methodsspline approximation methods

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) Numerical methods for integral equations (65R20) Integral operators (45P05) Integral operators (47G10) Numerical solutions to equations with linear operators (65J10) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Pseudodifferential operators (47G30)

Related Items (4)

The asymptotics of a Bessel-kernel determinant which arises in random matrix theory ⋮ Approximation numbers for the finite sections of Toeplitz operators with piecewise continuous symbols ⋮ More Than 40 Years of Algebraic Techniques in Numerical Analysis ⋮ Numerical analysis for one-dimensional Cauchy singular integral equations

Cites Work

• Spline qualocation methods for boundary integral equations
• The Calkin image of algebras of singular integral operators
• A symbol calculus for finite sections of singular integral operators with shift and piecewise continuous coefficients
• A general look at local principles with special emphasis on the norm computation aspect
• Algebras generated by idempotents and the symbol calculus for singular integral operators
• Stabilitätskriterien für Näherungsverfahren bei singulären Integralgleichungen in \(L^ p\)
• Spline approximation methods for multidimensional periodic pseudodifferential equations
• On spline approximation for a class of integral equations. I: Galerkin and collocation methods with piecewise polynomials
• A Banach Algebra Approach to the Stability of Projection Methods for Singular Integral Equations
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