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

作者：Graillat Stef^*; Menissier Morain Valerie

来源：Information and Computation, 2012, 216: 57-71.

DOI：10.1016/j.ic.2011.09.003

• Complex floating point arithmetic
• Error-free transformations
• Accurate summation
• Accurate dot product
• Accurate polynomial evaluation
• Homer's scheme
• High precision

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.

• 出版日期2012-7