Method to improve accuracy of numerical solutions to systems of linear equations
For broader coverage of this topic, see Iterative method.
This article is about iterative refinement in mathematics. For iterative refinement in software development, see Iterative and incremental development.
Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations.[1][2]
When solving a linear system due to the compounded accumulation of rounding errors, the computed solution may sometimes deviate from the exact solution Starting with iterative refinement computes a sequence which converges to when certain assumptions are met.
^Wilkinson, James H. (1963). Rounding Errors in Algebraic Processes. Englewood Cliffs, NJ: Prentice Hall.
^Moler, Cleve B. (April 1967). "Iterative refinement in floating point". Journal of the ACM. 14 (2). New York, NY: Association for Computing Machinery: 316–321. doi:10.1145/321386.321394.
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