منابع مشابه
Fast High Precision Summation ∗
Given a vector pi of floating-point numbers with exact sum s, we present a new algorithm with the following property: Either the result is a faithful rounding of s, or otherwise the result has a relative error not larger than epsKcond ( ∑ pi) for K to be specified. The statements are also true in the presence of underflow, the computing time does not depend on the exponent range, and no extra m...
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Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of exact real with value + error pair of floating-point numbers. Normally, value + error sum is more accurate than value alone, so error can estimate deviation between value and its exact target. Fast summation algorithm, that provides twofold sum of ∑...
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We present two new algorithms FastAccSum and FastPrecSum, one to compute a faithful rounding of the sum of floating-point numbers and the other for a result “as if” computed in K-fold precision. Faithful rounding means the computed result either is one of the immediate floating-point neighbors of the exact result or is equal to the exact sum if this is a floating-point number. The algorithms ar...
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Open problem: Is γ or exp(γ) rational ? Since the regular continued fraction gives best rational approximations, continued fraction computations can give theorems of the form: If x is rational, say x = p/q, then |q| > B for some (very large) bound B. To obtain a result like this with given bound B, we need to compute x with absolute error O(1/B2). Using this method we know that, if γ or exp(γ) ...
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Direct computation of the weighted sum of N complementary error functions at M points scales as O(M N). We present a O(M + N)-exact approximation algorithm to compute the same.
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ژورنال
عنوان ژورنال: Nonlinear Theory and Its Applications, IEICE
سال: 2010
ISSN: 2185-4106
DOI: 10.1587/nolta.1.2