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Ordering monomial factors of polynomials in the product representation

The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these roundi...

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Detalles Bibliográficos
Autores principales: Bunk, B., Elser, Stephan, Frezzotti, R., Jansen, K.
Lenguaje:eng
Publicado: 1998
Materias:
Acceso en línea:https://dx.doi.org/10.1016/S0010-4655(99)00198-8
http://cds.cern.ch/record/355690
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author Bunk, B.
Elser, Stephan
Frezzotti, R.
Jansen, K.
author_facet Bunk, B.
Elser, Stephan
Frezzotti, R.
Jansen, K.
author_sort Bunk, B.
collection CERN
description The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these rounding errors on the computation of polynomials approximating the function $1/s$. We consider polynomials both in a real variable $s$ and in a Hermitian matrix. By investigating several ordering schemes for the monomials of these polynomials, we finally demonstrate that there exist orderings of the monomials that keep rounding errors at a tolerable level.
id cern-355690
institution Organización Europea para la Investigación Nuclear
language eng
publishDate 1998
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spelling cern-3556902023-10-04T07:27:53Zdoi:10.1016/S0010-4655(99)00198-8http://cds.cern.ch/record/355690engBunk, B.Elser, StephanFrezzotti, R.Jansen, K.Ordering monomial factors of polynomials in the product representationParticle Physics - LatticeThe numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these rounding errors on the computation of polynomials approximating the function $1/s$. We consider polynomials both in a real variable $s$ and in a Hermitian matrix. By investigating several ordering schemes for the monomials of these polynomials, we finally demonstrate that there exist orderings of the monomials that keep rounding errors at a tolerable level.The numerical construction of polynomials in the product representation (as used for instance in variants of the multiboson technique) can become problematic if rounding errors induce an imprecise or even unstable evaluation of the polynomial. We give criteria to quantify the effects of these rounding errors on the computation of polynomials approximating the function $1/s$. We consider polynomials both in a real variable $s$ and in a Hermitian matrix. By investigating several ordering schemes for the monomials of these polynomials, we finally demonstrate that there exist orderings of the monomials that keep rounding errors at a tolerable level.hep-lat/9805026CERN-TH-98-127MPI-PHT-98-34CERN-TH-98-127MPI-PHT-98-34oai:cds.cern.ch:3556901998-05-27
spellingShingle Particle Physics - Lattice
Bunk, B.
Elser, Stephan
Frezzotti, R.
Jansen, K.
Ordering monomial factors of polynomials in the product representation
title Ordering monomial factors of polynomials in the product representation
title_full Ordering monomial factors of polynomials in the product representation
title_fullStr Ordering monomial factors of polynomials in the product representation
title_full_unstemmed Ordering monomial factors of polynomials in the product representation
title_short Ordering monomial factors of polynomials in the product representation
title_sort ordering monomial factors of polynomials in the product representation
topic Particle Physics - Lattice
url https://dx.doi.org/10.1016/S0010-4655(99)00198-8
http://cds.cern.ch/record/355690
work_keys_str_mv AT bunkb orderingmonomialfactorsofpolynomialsintheproductrepresentation
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AT frezzottir orderingmonomialfactorsofpolynomialsintheproductrepresentation
AT jansenk orderingmonomialfactorsofpolynomialsintheproductrepresentation