S0025 5718 1972 0309279 9

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mathematics of computation volume 26 number 118 april 1972 minimum norm differentiation formulas with improved roundoff error bounds by david k kahaner abstract numerical differentiation formulas of the form f ...

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...Mathematics of computation volume number april minimum norm differentiation formulas with improved roundoff error bounds by david k kahaner abstract numerical the form f i t we consider that have l wl ar d converge to m a as resulting can be several orders magnitude less than corresponding for high order differences introduction many computations require evaluation derivatives often function x is known at only discrete set points result another and some derivative needed usual situation approximate linear combination values v dj z summation over subset which computed even if were exactly ez sin its representation in finite word length computer involves more approximations contain substantial amounts these errors tend magnified process especially xt are close together estimating such procedure one finds answers become accurate first h decreased subsequently exhibit accuracy it therefore important rigorous bound on total select most appropriate value used obtained taking mth an interpola...

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Posted on: 27 Jan 2023 | 4 years ago
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