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minimize numerical error #4

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jannikmi opened this issue Jan 11, 2019 · 1 comment
Open

minimize numerical error #4

jannikmi opened this issue Jan 11, 2019 · 1 comment
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enhancement New feature or request help wanted Extra attention is needed

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@jannikmi
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jannikmi commented Jan 11, 2019

Optimise the factorisation such that it minimizes the numerical error during evaluation.
take the magnitude of the coefficients... into account during factorization.
The effects of Horner factorizations on the numerical error have been considered in

[3] J. M. Peña and T. Sauer, “On the multivariate Horner scheme”, SIAM journal on numerical analysis, vol. 37, no. 4, pp. 1186–1197, 2000.

[4] J. M. Peña and T. Sauer, “On the multivariate Horner scheme II: Running error analysis”, Computing, vol. 65, no. 4, pp. 313–322, 2000.

@jannikmi jannikmi added enhancement New feature or request help wanted Extra attention is needed labels May 19, 2019
@jannikmi
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jannikmi commented May 6, 2020

Note:
since v1.3.0 the coefficients are interchangeable per default. optimising the factorisation wrt. the coefficients might make a new independent version of the procedure necessary

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