Iterative refinement

Iterative refinement is an iterative method proposed by James H. Wilkinson to improve the accuracy of numerical solutions to systems of linear equations.

When solving a linear system $A x = b$ , due to the existence of rounding error, the computed solution $x ̂$ may sometimes deviate from the exact solution $x *$ . Starting with $x 0 = x ̂$ , iterative refinement computes a sequence ${x 0, x 1, x 2,\dots$ } which converges to $x *$ when certain assumptions are met.

References

Wilkinson, James H. (1963). Rounding Errors in Algebraic Processes. Englewood Cliffs, NJ: Prentice Hall.
Moler, Cleve B. (1967). "Iterative Refinement in Floating Point". Journal of the ACM. 14 (2). New York, NY: Association for Computing Machinery: 316–321. ISSN 0004-5411. {{cite journal}}: Unknown parameter |month= ignored (help)

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