TY - JOUR
T1 - Accurate Horner methods in real and complex floating-point arithmetic
AU - Cameron, Thomas R.
AU - Graillat, Stef
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer Nature B.V. 2024.
PY - 2024/6
Y1 - 2024/6
N2 - 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.
AB - 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.
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U2 - 10.1007/s10543-024-01017-w
DO - 10.1007/s10543-024-01017-w
M3 - Article
AN - SCOPUS:85188965986
SN - 0006-3835
VL - 64
JO - BIT Numerical Mathematics
JF - BIT Numerical Mathematics
IS - 2
M1 - 17
ER -