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Post-processing of Gauss–Seidel iterations

✍ Scribed by Michal Křížek; Liping Liu; Pekka Neittaanmäki

Book ID
101286586
Publisher
John Wiley and Sons
Year
1999
Tongue
English
Weight
66 KB
Volume
6
Category
Article
ISSN
1070-5325

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✦ Synopsis

We examine a simple post-processing technique when solving the system of n linear algebraic equations Ax = b with a nonsingular matrix using the classical iterative methods such as the Gauss-Seidel method. We prove that this technique accelerates the convergence of iterations. Its efficiency is demonstrated on a system arising from a finite element approximation of a second order elliptic boundary value problem.

📜 SIMILAR VOLUMES

Improving Jacobi and Gauss-Seidel Iterat
Improving Jacobi and Gauss-Seidel Iterations
✍ J.P. Milaszewicz 📂 Article 📅 1987 🏛 Elsevier Science 🌐 English ⚖ 500 KB

When convergent Jacobi or Gauss-Seidel iterations can be applied to solve systems of linear equations, a natural question is how convergence rates are affected if the original system is modified by performing some Gaussian elimination. We prove that if the initial iteration matrix is nonnegative, th