The Pad\'e iterations for the matrix sign function and their reciprocals are optimal
classification
🧮 math.NA
keywords
iterationsfunctionreciprocalssignconvergingdegreesdenominatorlocally
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It is proved that among the rational iterations locally converging with order s>1 to the sign function, the Pad\'e iterations and their reciprocals are the unique rationals with the lowest sum of the degrees of numerator and denominator.
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