On the accurate computation of the Newton form of the Lagrange interpolant

In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this frame...

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Published in:	Numerical algorithms Vol. 98; no. 3; pp. 1553 - 1573
Main Authors:	Khiar, Y., Mainar, E., Royo-Amondarain, E., Rubio, B.
Format:	Journal Article
Language:	English
Published:	New York Springer US 01.03.2025 Springer Nature B.V
Subjects:	Accuracy Algebra Algorithms Collocation Collocation methods Computation Computer Science Factorization Linear algebra Mathematical analysis Numeric Computing Numerical Analysis Original Paper Polynomials Recursive functions Theory of Computation Divided differences Bidiagonal decompositions Lagrange interpolation 15A23 Totally positive matrices 15A06 65F15 High relative accuracy 65F05 Newton basis 15A18
ISSN:	1017-1398, 1572-9265
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Abstract	In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this framework, the present work provides the factorization of the collocation matrices of Newton bases—of relevance when considering the Lagrange interpolation problem—together with an algorithm that allows to numerically compute it to high relative accuracy. This further allows to determine the coefficients of the interpolating polynomial and to compute the singular values and the inverse of the collocation matrix. Conditions that guarantee high relative accuracy for these methods and, in the former case, for the classical recursion formula of divided differences, are determined. Numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed. Finally, numerical experiments illustrate the accuracy and effectiveness of the proposed methods with several algebraic problems, in stark contrast with traditional approaches.
AbstractList	In recent years many efforts have been devoted to finding bidiagonal factorizations of nonsingular totally positive matrices, since their accurate computation allows to numerically solve several important algebraic problems with great precision, even for large ill-conditioned matrices. In this framework, the present work provides the factorization of the collocation matrices of Newton bases—of relevance when considering the Lagrange interpolation problem—together with an algorithm that allows to numerically compute it to high relative accuracy. This further allows to determine the coefficients of the interpolating polynomial and to compute the singular values and the inverse of the collocation matrix. Conditions that guarantee high relative accuracy for these methods and, in the former case, for the classical recursion formula of divided differences, are determined. Numerical errors due to imprecise computer arithmetic or perturbed input data in the computation of the factorization are analyzed. Finally, numerical experiments illustrate the accuracy and effectiveness of the proposed methods with several algebraic problems, in stark contrast with traditional approaches.
Author	Khiar, Y. Rubio, B. Mainar, E. Royo-Amondarain, E.
Author_xml	– sequence: 1 givenname: Y. surname: Khiar fullname: Khiar, Y. organization: Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza – sequence: 2 givenname: E. surname: Mainar fullname: Mainar, E. organization: Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza – sequence: 3 givenname: E. surname: Royo-Amondarain fullname: Royo-Amondarain, E. email: eduroyo@unizar.es organization: Departamento de Matemáticas/CAPA, Universidad de Zaragoza – sequence: 4 givenname: B. surname: Rubio fullname: Rubio, B. organization: Departamento de Matemática Aplicada/IUMA, Universidad de Zaragoza
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References	JM Carnicer (1843_CR3) 2015 J Delgado (1843_CR5) 2019; 80 1843_CR30 A Marco (1843_CR26) 2017; 75 T Ando (1843_CR1) 1987; 90 M Gasca (1843_CR11) 1994; 202 H Tal-Ezer (1843_CR31) 1991; 12 A Marco (1843_CR25) 2017; 517 1843_CR16 M Gasca (1843_CR10) 1992; 165 A Marco (1843_CR27) 2022; 651 P Koev (1843_CR14) 2005; 27 A Marco (1843_CR28) 2024; 31 JP Berrut (1843_CR2) 2004; 46 A Marco (1843_CR24) 2019; 350 P Koev (1843_CR15) 2007; 29 M Gasca (1843_CR12) 1996 E Mainar (1843_CR20) 2022; 116 B Fischer (1843_CR9) 1989; 53 1843_CR21 E Mainar (1843_CR17) 2018; 25 J Demmel (1843_CR6) 2005; 27 A Marco (1843_CR23) 2016; 495 T Finck (1843_CR8) 1993; 183 H Oruç (1843_CR29) 2000; 315 J Delgado (1843_CR4) 2019; 26 A Marco (1843_CR22) 2013; 26 E Mainar (1843_CR19) 2022; 48 J Demmel (1843_CR7) 2006; 27 E Mainar (1843_CR18) 2021; 87 NJ Higham (1843_CR13) 2002
References_xml	– volume: 165 start-page: 25 year: 1992 ident: 1843_CR10 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(92)90226-Z – volume: 315 start-page: 113 year: 2000 ident: 1843_CR29 publication-title: Linear Algebra Appl. doi: 10.1016/S0024-3795(00)00124-5 – ident: 1843_CR21 doi: 10.1007/s11075-023-01588-9 – volume: 31 start-page: e2527 issue: 1 year: 2024 ident: 1843_CR28 publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.2527 – volume: 202 start-page: 33 year: 1994 ident: 1843_CR11 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(94)90183-X – volume: 12 start-page: 648 year: 1991 ident: 1843_CR31 publication-title: SIAM J. Sci. Statist. Comput. doi: 10.1137/0912034 – volume: 27 start-page: 382 year: 2006 ident: 1843_CR7 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2005.09.014 – volume: 46 start-page: 501 year: 2004 ident: 1843_CR2 publication-title: SIAM Rev. doi: 10.1137/S0036144502417715 – volume: 53 start-page: 265 year: 1989 ident: 1843_CR9 publication-title: Math. Comp. – volume: 26 start-page: e2217 issue: 10 year: 2019 ident: 1843_CR4 publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.2217 – volume: 183 start-page: 179 year: 1993 ident: 1843_CR8 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(93)90431-M – volume: 116 start-page: 126 year: 2022 ident: 1843_CR20 publication-title: Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat doi: 10.1007/s13398-022-01253-1 – volume: 27 start-page: 42 year: 2005 ident: 1843_CR6 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479804440335 – volume: 48 start-page: 38 year: 2022 ident: 1843_CR19 publication-title: Adv. Comput. Math. doi: 10.1007/s10444-022-09954-2 – volume: 90 start-page: 165 year: 1987 ident: 1843_CR1 publication-title: Linear Algebra Appl. doi: 10.1016/0024-3795(87)90313-2 – start-page: 53 volume-title: Thirteenth International Conference Zaragoza-Pau on Mathematics and its Applications year: 2015 ident: 1843_CR3 – volume: 29 start-page: 731 year: 2007 ident: 1843_CR15 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/04061903X – volume: 26 start-page: 357 year: 2013 ident: 1843_CR22 publication-title: Electron. J. Linear Algebra doi: 10.13001/1081-3810.1658 – volume-title: Accuracy and stability of numerical algorithms year: 2002 ident: 1843_CR13 doi: 10.1137/1.9780898718027 – volume: 651 start-page: 312 year: 2022 ident: 1843_CR27 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2022.06.023 – ident: 1843_CR16 – ident: 1843_CR30 – volume: 25 start-page: e2184 year: 2018 ident: 1843_CR17 publication-title: Numer. Linear Algebra Appl. doi: 10.1002/nla.2184 – volume: 87 start-page: 77 year: 2021 ident: 1843_CR18 publication-title: J. Sci. Comput. doi: 10.1007/s10915-021-01500-4 – volume: 27 start-page: 1 year: 2005 ident: 1843_CR14 publication-title: SIAM J. Matrix Anal. Appl. doi: 10.1137/S0895479803438225 – volume: 80 start-page: 1264 year: 2019 ident: 1843_CR5 publication-title: J. Sci. Comput. doi: 10.1007/s10915-019-00975-6 – volume-title: Total Positivity and Its Applications, pp 109–130 year: 1996 ident: 1843_CR12 doi: 10.1007/978-94-015-8674-0 – volume: 495 start-page: 90 year: 2016 ident: 1843_CR23 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2016.01.037 – volume: 75 start-page: 655 year: 2017 ident: 1843_CR26 publication-title: Numer. Algor. doi: 10.1007/s11075-016-0215-7 – volume: 350 start-page: 299 year: 2019 ident: 1843_CR24 publication-title: J. Comput. Appl. Math. doi: 10.1016/j.cam.2018.10.009 – volume: 517 start-page: 63 year: 2017 ident: 1843_CR25 publication-title: Linear Algebra Appl. doi: 10.1016/j.laa.2016.12.003
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SubjectTerms	Accuracy Algebra Algorithms Collocation Collocation methods Computation Computer Science Factorization Linear algebra Mathematical analysis Numeric Computing Numerical Analysis Original Paper Polynomials Recursive functions Theory of Computation
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Title	On the accurate computation of the Newton form of the Lagrange interpolant
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