Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic
| Autor: | Stef Graillat, Valérie Ménissier-Morain |
|---|---|
| Přispěvatelé: | Performance et Qualité des Algorithmes Numériques (PEQUAN), Laboratoire d'Informatique de Paris 6 (LIP6), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS) |
| Rok vydání: | 2012 |
| Předmět: |
Kahan summation algorithm
Polynomial Floating point Accurate summation Error-free transformations 010103 numerical & computational mathematics Minifloat 01 natural sciences Theoretical Computer Science Accurate dot product High precision [INFO]Computer Science [cs] Hardware_ARITHMETICANDLOGICSTRUCTURES 0101 mathematics Arithmetic Mathematics Hornerʼs scheme Dot product Extended precision Computer Science Applications 010101 applied mathematics Computational Theory and Mathematics Multiplication Pairwise summation Complex floating point arithmetic Accurate polynomial evaluation Information Systems |
| Zdroj: | Information and Computation Information and Computation, 2012, 216, pp.57-71. ⟨10.1016/j.ic.2011.09.003⟩ Information and Computation, Elsevier, 2012, pp.57-71. ⟨10.1016/j.ic.2011.09.003⟩ |
| ISSN: | 0890-5401 1090-2651 |
| DOI: | 10.1016/j.ic.2011.09.003 |
| Popis: | International audience; Several different techniques and softwares intend to improve the accuracy of resultscomputed in a fixed finite precision. Here we focus on methods to improve the accuracyof summation, dot product and polynomial evaluation. Such algorithms exist real floatingpoint numbers. In this paper, we provide new algorithms which deal with complex floatingpoint numbers. We show that the computed results are as accurate as if computed intwice the working precision. The algorithms are simple since they only require additionsubtraction and multiplication of floating point numbers in the same working precision asthe given data. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect