TY - JOUR UR - http://lib.ugent.be/catalog/pug01:3108575 ID - pug01:3108575 LA - eng TI - O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing PY - 2012 JO - (2012) SIAM JOURNAL ON SCIENTIFIC COMPUTING SN - 1064-8275 PB - 2012 AU - Bogaert, Ignace UGent 001999169491 801001844572 AU - Michiels, Bart UGent 002004076681 802000613055 AU - Fostier, Jan TW05 002000085537 801002005432 0000-0002-9994-8269 AB - A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1]. More specifically the time required to evaluate any Legendre polynomial, regardless of argument and degree, is bounded by a constant; i.e., the complexity is O(1). The proposed algorithm also immediately yields an O(1) algorithm for computing an arbitrary Gauss-Legendre quadrature node. Such a capability is crucial for efficiently performing certain parallel computations with high order Legendre polynomials, such as computing an integral in parallel by means of Gauss-Legendre quadrature and the parallel evaluation of Legendre series. In order to achieve the O(1) complexity, novel efficient asymptotic expansions are derived and used alongside known results. A C++ implementation is available from the authors that includes the evaluation routines of the Legendre polynomials and Gauss-Legendre quadrature rules. ER -Download RIS file
00000nam^a2200301^i^4500 | |||
001 | 3108575 | ||
005 | 20180813142144.0 | ||
008 | 130125s2012------------------------eng-- | ||
022 | a 1064-8275 | ||
024 | a 000310474400033 2 wos | ||
024 | a 1854/LU-3108575 2 handle | ||
024 | a 10.1137/110855442 2 doi | ||
040 | a UGent | ||
245 | a O(1) Computation of Legendre polynomials and Gauss-Legendre nodes and weights for parallel computing | ||
260 | c 2012 | ||
520 | a A self-contained set of algorithms is proposed for the fast evaluation of Legendre polynomials of arbitrary degree and argument is an element of [-1, 1]. More specifically the time required to evaluate any Legendre polynomial, regardless of argument and degree, is bounded by a constant; i.e., the complexity is O(1). The proposed algorithm also immediately yields an O(1) algorithm for computing an arbitrary Gauss-Legendre quadrature node. Such a capability is crucial for efficiently performing certain parallel computations with high order Legendre polynomials, such as computing an integral in parallel by means of Gauss-Legendre quadrature and the parallel evaluation of Legendre series. In order to achieve the O(1) complexity, novel efficient asymptotic expansions are derived and used alongside known results. A C++ implementation is available from the authors that includes the evaluation routines of the Legendre polynomials and Gauss-Legendre quadrature rules. | ||
598 | a A1 | ||
100 | a Bogaert, Ignace u UGent 0 001999169491 0 801001844572 0 974829877146 | ||
700 | a Michiels, Bart u UGent 0 002004076681 0 802000613055 0 971438786246 | ||
700 | a Fostier, Jan u TW05 0 002000085537 0 801002005432 0 0000-0002-9994-8269 | ||
650 | a Technology and Engineering | ||
653 | a Gauss-Legendre quadrature | ||
653 | a Legendre polynomial | ||
653 | a fixed complexity | ||
653 | a parallel computing | ||
653 | a QUADRATURE | ||
773 | t SIAM JOURNAL ON SCIENTIFIC COMPUTING g SIAM J. Sci. Comput. 2012. 34 (3) p.C83-C101 q 34:3<C83 | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/3108575/file/3108617 z [ugent] y EM_996.pdf | ||
856 | 3 Full Text u https://biblio.ugent.be/publication/3108575/file/3108618 z [open] y EM_996a.pdf | ||
920 | a article | ||
852 | x EA b TW05 | ||
922 | a UGENT-EA |
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