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Fast verified solutions of linear systems. (English) Zbl 1184.65046

Summary: This paper aims to survey fast methods of verifying the accuracy of a numerical solution of a linear system. For the last decade, a number of fast verification algorithms have been proposed to obtain an error bound of a numerical solution of a dense or sparse linear system. Such fast algorithms rely on the verified numerical computation using floating-point arithmetic defined by IEEE standard 754. Some fast verification methods for dense and sparse linear systems are reviewed together with corresponding numerical results to show the practical use and efficiency of the verified numerical computation as much as possible.

MSC:

65F30 Other matrix algorithms (MSC2010)
65G20 Algorithms with automatic result verification
65G30 Interval and finite arithmetic

Software:

mctoolbox; INTLAB

References:

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