ORTHPOL swMATH ID: 659 Software Authors: Gautschi, Walter Description: Algorithm 726: ORTHPOL - A package of routines for generating orthogonal polynomials and Gauss‐type quadrature rules. A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the coefficients in the three-term recurrence relation satisfied by the orthogonal polynomials. Once these are known, additional data can be generated, such as zeros of orthogonal polynomials and Gauss-type quadrature rules, for which routines are also provided. Homepage: http://dl.acm.org/citation.cfm?id=174605 Keywords: quadrature rules; Gauss-type rules; orthogonal polynomials; correction Related Software: OPQ; Matlab; QUADPACK; OrthogonalPolynomials; GQRAT; mctoolbox; GQLOG; GitHub; Octave; FastGaussQuadrature; Chebfun; EXTEND; Algorithm 719; RADAU; R; outliers; dixonr; DixonText.CriticalValues; Excel; JuliBootS Cited in: 80 Publications Standard Articles 2 Publications describing the Software, including 2 Publications in zbMATH Year Remark on Algorithm 726: ORTHPOL – a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. Zbl 0932.65018Gautschi, Walter 1998 Algorithm 726: ORTHPOL – a package for routines for generating orthogonal polynomials and Gauss-type quadrature rules. Zbl 0888.65013Gautschi, W. 1994 all top 5 Cited by 108 Authors 11 Gautschi, Walter 6 Milovanović, Gradimir V. 5 Cai, Wei 5 Cvetković, Aleksandar S. 5 Deng, Shaozhong 4 Laurie, Dirk P. 3 Alkhatib, Ali 3 Guessab, Allal 3 Jacobs, Donald J. 3 Notaris, Sotirios E. 2 Chen, Wei 2 Damelin, Steven Benjamin 2 Diethelm, Kai 2 Gout, Christian 2 Lee, Sanghoon 1 Ahlfeld, Richard 1 Arceci, Luca 1 Babaei, Masoud 1 Baxter, Brad J. C. 1 Baye, Daniel 1 Behan, Connor 1 Belhadjsalah, Hédi 1 Belkouchi, B. 1 Bigoni, Daniele 1 Bilionis, Ilias 1 Bultheel, Adhemar François 1 Chan, Stephanie 1 Chang, Yoon-Suk 1 Choi, Jae-Boong 1 Costabile, Francesco Aldo 1 Cruz-Barroso, Ruymán 1 da Rocha, Zélia 1 Deckers, Karl 1 Dorao, Carlos A. 1 Dresse, Zoé 1 Ege, Serife Muge 1 Engsig-Karup, Allan P. 1 Ernst, Darin R. 1 Eskilsson, Claes 1 Ezzirani, Abdelkrim 1 Fermo, Luisa 1 Fischer, Hans-Jürgen 1 Gervasio, Paola 1 Gualtieri, Maria Italia 1 Gustafson, Sven-Åke 1 Hale, Nicholas 1 Higham, Nicholas J. 1 Horstemeyer, Mark F. 1 Jakobsen, Hugo Atle 1 Johnson, Robert W. 1 Karniadakis, George Em 1 Karp, Alan H. 1 Kayijuka, Idrissa 1 Kim, Youngjin 1 Kohn, Lucas 1 Konuralp, Ali 1 Kuijlaars, Arno B. J. 1 Kwak, Byung Man 1 Landreman, Matt 1 Lee, Dockjin 1 Li, Shikang 1 Lindgren, Lars-Erik 1 Liu, Wing Kam 1 Liu, Zexin 1 Lombardi, Guido 1 Magnus, Alphonse Ph. 1 Mastroianni, Giuseppe 1 Melendo, Begoña 1 Mesquita, Teresa A. 1 Meurant, Gérard A. 1 Miller, Robert E. 1 Montomoli, Francesco 1 Morrison, Conor L. 1 Mougaida, Ahlem 1 Napoli, Anna 1 Narayan, Akil C. 1 Notarangelo, Incoronata 1 Olson, Gregory B. 1 Pan, Indranil 1 Patterson, Thomas N. L. 1 Qin, Peihua 1 Quarteroni, Alfio M. 1 Rahman, Qazi Ibadur 1 Rosengren, Hjalmar 1 Roussos, George 1 Russomanno, Angelo 1 Sacco, Riccardo 1 Saleri, Fausto 1 Santoro, Giuseppe E. 1 Shizgal, Bernard 1 Shizgal, Bernie D. 1 Siad, Larbi 1 Sidi, Avram 1 Sommariva, Alvise 1 Stanić, Marija P. 1 Tian, Rong 1 Topal, Fatma Serap 1 Townsend, Alex 1 Vabishchevich, Pëtr Nikolaevich 1 Van Assche, Walter ...and 8 more Authors all top 5 Cited in 39 Serials 12 Journal of Computational and Applied Mathematics 6 Mathematics of Computation 5 ACM Transactions on Mathematical Software 4 Journal of Computational Physics 4 Numerical Algorithms 3 Journal of Scientific Computing 3 SIAM Journal on Scientific Computing 3 Computational Geosciences 2 Computers & Mathematics with Applications 2 Computer Physics Communications 2 BIT 2 International Journal for Numerical Methods in Engineering 2 Journal of Approximation Theory 2 Applied Numerical Mathematics 2 Journal of Integral Equations and Applications 2 Communications in Computational Physics 1 International Journal of Engineering Science 1 Journal of Engineering Mathematics 1 Journal of Statistical Physics 1 Physics Reports 1 Applied Mathematics and Computation 1 Calcolo 1 Mathematics and Computers in Simulation 1 Numerical Functional Analysis and Optimization 1 Numerische Mathematik 1 Zeitschrift für Analysis und ihre Anwendungen 1 Mathematical and Computer Modelling 1 SIAM Journal on Matrix Analysis and Applications 1 European Journal of Operational Research 1 Advances in Computational Mathematics 1 Opuscula Mathematica 1 Journal of Mathematical Chemistry 1 The Ramanujan Journal 1 Computational Methods in Applied Mathematics 1 Structural and Multidisciplinary Optimization 1 Mediterranean Journal of Mathematics 1 International Journal of Numerical Analysis and Modeling 1 Journal of Statistical Mechanics: Theory and Experiment 1 Unitext all top 5 Cited in 25 Fields 59 Numerical analysis (65-XX) 30 Approximations and expansions (41-XX) 17 Harmonic analysis on Euclidean spaces (42-XX) 12 Special functions (33-XX) 5 Optics, electromagnetic theory (78-XX) 5 Operations research, mathematical programming (90-XX) 4 Partial differential equations (35-XX) 4 Integral equations (45-XX) 4 Fluid mechanics (76-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 3 Biology and other natural sciences (92-XX) 2 Number theory (11-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Probability theory and stochastic processes (60-XX) 2 Statistics (62-XX) 2 Mechanics of deformable solids (74-XX) 2 Geophysics (86-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Functions of a complex variable (30-XX) 1 Operator theory (47-XX) 1 Relativity and gravitational theory (83-XX) 1 Astronomy and astrophysics (85-XX) 1 Systems theory; control (93-XX) Citations by Year