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Published in:
2021 | OriginalPaper | Chapter
5. Iterative Methods for Systems of Linear Equations
Authors : Peter Knabner, Lutz Angermann
Published in: Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Publisher: Springer International Publishing
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Abstract
We consider again the system of linear equations with nonsingular matrix \(A \in \mathbb {R}^{m,m}\), right-hand side \(b \in \mathbb {R}^m\), and solution \(x\in \mathbb {R}^m\). As shown in Chapters 2 and 3, such systems of equations arise from finite element discretizations of elliptic boundary value problems. The matrix A is the stiffness matrix and thus sparse, as can be seen from (2.41).