Accurate summation, dot product and polynomial evaluation in complex floating point arithmetic

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• 作者：Stef Graillat ; ^{stef.graillat@lip6.fr} ; Val&eacute ; rie M&eacute ; nissier-Morain¹ ; ^{valerie.menissier-morain@lip6.fr}
• 关键词：Complex floating point arithmetic ; Error-free transformations ; Accurate summation ; Accurate dot product ; Accurate polynomial evaluation ; Horner始s scheme ; High precision
• 刊名：Information and Computation
• 出版年：2012
• 期刊代码：132_08905401
• 类别：cp
• 出版时间：July, 2012
• 卷：216
• 期：Complete
• 页码：57-71
• 文件大小：302 K

摘要

Several different techniques and softwares intend to improve the accuracy of results computed in a fixed finite precision. Here we focus on methods to improve the accuracy of summation, dot product and polynomial evaluation. Such algorithms exist real floating point numbers. In this paper, we provide new algorithms which deal with complex floating point numbers. We show that the computed results are as accurate as if computed in twice the working precision. The algorithms are simple since they only require addition, subtraction and multiplication of floating point numbers in the same working precision as the given data.