Accurate Horner methods in real and complex floating-point arithmetic

Thomas R. Cameron, Stef Graillat

Research output: Contribution to journalArticlepeer-review


In this article, we derive accurate Horner methods in real and complex floating-point arithmetic. In particular, we show that these methods are as accurate as if computed in k-fold precision and then rounded into the working precision. When k is two, our methods are comparable or faster than the existing compensated Horner routines. When compared to multi-precision software, such as MPFR and MPC, our methods are significantly faster, up to k equal to eight, that is, up to 489 bits in the significand.

Original languageEnglish (US)
Article number17
JournalBIT Numerical Mathematics
Issue number2
StatePublished - Jun 2024

All Science Journal Classification (ASJC) codes

  • Software
  • Computer Networks and Communications
  • Computational Mathematics
  • Applied Mathematics

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