Accurate Horner methods in real and complex floating-point arithmetic
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 ex...
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| Veröffentlicht in: | BIT 2024-06, Vol.64 (2), Article 17 |
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| creator | Cameron, Thomas R. Graillat, Stef |
| description | 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. |
| doi_str_mv | 10.1007/s10543-024-01017-w |
| format | Article |
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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
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k
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k
-fold precision and then rounded into the working precision. When
k
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| subjects | Computational Mathematics and Numerical Analysis Floating point arithmetic Mathematics Mathematics and Statistics Numeric Computing |
| title | Accurate Horner methods in real and complex floating-point arithmetic |
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