On Some Iterative Methods for Solving Elliptic Difference Equations (Classic Reprint) - Hardcover

Herbert B. Keller

 
9780266693413: On Some Iterative Methods for Solving Elliptic Difference Equations (Classic Reprint)

Synopsis

Explore a general framework of iterative methods for solving large elliptic difference equations and learn how to pick the best scheme for speed and stability.

This book presents a family of iterative schemes tailored to common five-point Laplace grids. It explains how eigenvalues guide convergence, introduces complete image classes, and shows how to relate different schemes to a reference method. A detailed treatment of Laplace’s equation demonstrates practical application and how known convergence results arise from the theory.

  • Learn how to model and analyze iterative methods using eigenvalues and matrix splittings.
  • See how reference schemes and their “images” help identify the best performing methods.
  • Explore complete image classes and how they cover many established and generalized schemes.
  • Review a concrete example with Laplace’s equation to connect theory to computation.
Ideal for readers of numerical analysis and computational mathematics seeking a clear path to efficient, reliable iterative solvers.

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