{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,11,29]],"date-time":"2024-11-29T13:40:22Z","timestamp":1732887622913,"version":"3.30.0"},"reference-count":16,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T00:00:00Z","timestamp":1706313600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T00:00:00Z","timestamp":1706313600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[2024,12]]},"DOI":"10.1007\/s11075-024-01761-8","type":"journal-article","created":{"date-parts":[[2024,1,27]],"date-time":"2024-01-27T04:31:11Z","timestamp":1706329871000},"page":"1535-1561","update-policy":"http:\/\/dx.doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Extended homogeneous bivariate orthogonal polynomials: symbolic and numerical Gaussian cubature formula"],"prefix":"10.1007","volume":"97","author":[{"given":"Jilali","family":"Abouir","sequence":"first","affiliation":[]},{"given":"Brahim","family":"Benouahmane","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2024,1,27]]},"reference":[{"issue":"1\u20132","key":"1761_CR1","first-page":"29","volume":"10","author":"J Abouir","year":"2018","unstructured":"Abouir, J., Benouahmane, B.: Multivariate homogeneous two-point Pad\u00e9 approximants. Jaen J. Approx. 10(1\u20132), 29\u201348 (2018)","journal-title":"Jaen J. Approx."},{"key":"1761_CR2","doi-asserted-by":"publisher","first-page":"432","DOI":"10.1553\/etna_vol58s432","volume":"58","author":"J Abouir","year":"2023","unstructured":"Abouir, J., Benouahmane, B., Chakir, Y.: Rational symbolic cubature rules over the first quadrant in a cartesian plane. Electron. Trans. Numer. Anal. 58, 432\u2013449 (2023)","journal-title":"Electron. Trans. Numer. Anal."},{"key":"1761_CR3","doi-asserted-by":"publisher","first-page":"1254","DOI":"10.1109\/TAC.2009.2019800","volume":"54","author":"I Arasaratnam","year":"2009","unstructured":"Arasaratnam, I., Haykin, S.: Cubature Kalman filters. IEEE Trans. Automat. Control. 54, 1254\u20131269 (2009)","journal-title":"IEEE Trans. Automat. Control."},{"key":"1761_CR4","doi-asserted-by":"publisher","first-page":"157","DOI":"10.1016\/j.automatica.2018.11.041","volume":"101","author":"D Ballreich","year":"2019","unstructured":"Ballreich, D.: Stable and efficient cubature rules by metaheuristic optimization with application to Kalman filtering. Automatica 101, 157\u2013165 (2019)","journal-title":"Automatica"},{"key":"1761_CR5","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1006\/jath.2000.3565","volume":"113","author":"B Benouahmane","year":"2001","unstructured":"Benouahmane, B., Cuyt, A.: Properties of multivariate homogeneous orthogonal polynomials. J. Approx. Theory 113, 1\u201320 (2001)","journal-title":"J. Approx. Theory"},{"issue":"1\u20132","key":"1761_CR6","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1023\/A:1019128823463","volume":"24","author":"B Benouahmane","year":"2000","unstructured":"Benouahmane, B., Cuyt, A.: Multivariate orthogonal polynomials, homogeneous Pad\u00e9 approximants and Gaussian cubature. Numer. Algorithms 24(1\u20132), 1\u201315 (2000)","journal-title":"Numer. Algorithms"},{"key":"1761_CR7","doi-asserted-by":"crossref","unstructured":"Brezinski, C.: Pad\u00e9-type Approximation and General Orthogonal Polynomials. ISNM 50, Birkh\u00e4user Verlag, Basel, 67\u2013105 (1980)","DOI":"10.1007\/978-3-0348-6558-6"},{"key":"1761_CR8","doi-asserted-by":"crossref","unstructured":"Chakir, Y., Abouir, J., Benouahmane, B.: Multivariate homogeneous two-point Pad\u00e9 approximants and continued fractions. Comp. Appl. Math. 39(15) (2020)","DOI":"10.1007\/s40314-019-0929-y"},{"key":"1761_CR9","doi-asserted-by":"crossref","unstructured":"Cools, R.: Constructing cubature formulas: the science behind the art. Acta Numer. 1\u201353 (1997)","DOI":"10.1017\/S0962492900002701"},{"key":"1761_CR10","doi-asserted-by":"crossref","unstructured":"Cuyt, A., Benouahmane, B., Hamsapriye, Yaman, I.: Symbolic-numeric Gaussian cubature rules. Appl. Numer. Math. 61(8), 929\u2013945 (2011)","DOI":"10.1016\/j.apnum.2011.03.003"},{"key":"1761_CR11","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1016\/S0377-0427(99)00028-X","volume":"105","author":"A Cuyt","year":"1999","unstructured":"Cuyt, A.: How well can the concept of Pad\u00e9 approximant be generalized to the multivariate case? J. Comput. Appl. Math. 105, 25\u201350 (1999)","journal-title":"J. Comput. Appl. Math."},{"issue":"252","key":"1761_CR12","doi-asserted-by":"publisher","first-page":"1843","DOI":"10.1090\/S0025-5718-05-01763-1","volume":"74","author":"C D\u00edaz-Mendoza","year":"2005","unstructured":"D\u00edaz-Mendoza, C., Gonz\u00e1lez-Vera, P., Jim\u00e9nez-Paiz, M.: Strong Stieltjes distributions and orthogonal Laurent polynomials with applications to quadrature and Pad\u00e9 approximation. Math. Comput. 74(252), 1843\u20131870 (2005)","journal-title":"Math. Comput."},{"issue":"3","key":"1761_CR13","doi-asserted-by":"publisher","first-page":"747","DOI":"10.1006\/jmaa.1996.0345","volume":"202","author":"P Gonz\u00e1lez-Vera","year":"1996","unstructured":"Gonz\u00e1lez-Vera, P., Paiz, M.J., Orive, R., Lagomasino, G.L.: On the Convergence of Quadrature Formulas Connected with Multipoint Pad\u00e9-Type Approximation. J. Math. Anal. Appl. 202(3), 747\u2013775 (1996)","journal-title":"J. Math. Anal. Appl."},{"key":"1761_CR14","doi-asserted-by":"publisher","first-page":"316","DOI":"10.1137\/0513023","volume":"13","author":"MA Kowalski","year":"1982","unstructured":"Kowalski, M.A.: Orthogonality and recursion formulas for polynomials in $$n$$ variables. SIAM J. Math. Anal. 13, 316\u2013323 (1982)","journal-title":"SIAM J. Math. Anal."},{"key":"1761_CR15","doi-asserted-by":"publisher","first-page":"426","DOI":"10.1553\/etna_vol53s426","volume":"53","author":"R Orive","year":"2020","unstructured":"Orive, R., Santos-Le\u00f3n, J.C., Miodrag, M., Spalevi\u0107, M.: Cubature formulae for the Gaussian weight. Some old and new rules. ETNA 53, 426\u2013438 (2020)","journal-title":"ETNA"},{"key":"1761_CR16","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2021.109541","volume":"127","author":"JC Santos-Le\u00f3n","year":"2021","unstructured":"Santos-Le\u00f3n, J.C., Orive, R., Acosta, D., Acosta, L.: The Cubature Kalman Filter revisited. Automatica 127, 109541 (2021)","journal-title":"Automatica"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01761-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11075-024-01761-8\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11075-024-01761-8.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T09:22:30Z","timestamp":1732785750000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11075-024-01761-8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,1,27]]},"references-count":16,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12]]}},"alternative-id":["1761"],"URL":"https:\/\/doi.org\/10.1007\/s11075-024-01761-8","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2024,1,27]]},"assertion":[{"value":"8 June 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 January 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"27 January 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}