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Perturbation methods for the solution of linear problems

Part of the Lecture Notes in Mathematics book series (LNM,volume 701)

Abstract

Linear problems of central interest in numerical analysis are the solution of linear equations, the construction of the inverse or a generalized inverse of a linear operator, finding the eigenvalues and eigenvectors of a linear operator, and linear programming. A survey is made of methods which apply if the data of a solved linear problem is perturbed by operators and vectors of small norm (analytic perturbation), or by operators of finite rank and vectors belonging to a finite-dimensional subspace (algebraic perturbation). Perturbation methods may be used to extend the theory of linear problems, to estimate errors due to inaccurate data and computation, and to solve perturbed problems with economy of effort.

Keywords

  • Linear Operator
  • Perturbation Method
  • Linear Problem
  • Generalize Inverse
  • Analytic Perturbation

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Dedicated to Professor Arvid T. Lonseth on his 65th Birthday

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Rall, L.B. (1979). Perturbation methods for the solution of linear problems. In: Nashed, M.Z. (eds) Functional Analysis Methods in Numerical Analysis. Lecture Notes in Mathematics, vol 701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062084

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  • DOI: https://doi.org/10.1007/BFb0062084

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