Iterative Re nement and LAPACKN
نویسندگان
چکیده
The technique of iterative reenement for improving the computed solution to a linear system was used on desk calculators and computers in the 1940s and has remained popular. In the 1990s iterative reenement is well supported in software libraries, notably in LAPACK. Although the behaviour of iterative re-nement in oating point arithmetic is reasonably well understood, the existing theory is not suucient to justify the use of xed precision iterative reenement in all the LAPACK routines in which it is implemented. We present analysis that provides the theoretical support needed for LAPACK. The analysis covers both mixed and xed precision iterative reenement with an arbitrary number of iterations, makes only a general assumption on the underlying solver, and is relatively short. We identify some remaining open problems.
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