{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,7]],"date-time":"2025-10-07T11:48:22Z","timestamp":1759837702209},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[1993,6,1]],"date-time":"1993-06-01T00:00:00Z","timestamp":738892800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Adv Comput Math"],"published-print":{"date-parts":[[1993,6]]},"DOI":"10.1007\/bf02071388","type":"journal-article","created":{"date-parts":[[2005,8,13]],"date-time":"2005-08-13T11:53:36Z","timestamp":1123934016000},"page":"241-258","source":"Crossref","is-referenced-by-count":10,"title":["Construction of polynomials that are orthogonal with respect to a discrete bilinear form"],"prefix":"10.1007","volume":"1","author":[{"given":"Lothar","family":"Reichel","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02071388_CR1","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1016\/0024-3795(88)90158-9","volume":"98","author":"S.T. Alexander","year":"1988","unstructured":"S.T. Alexander, C.T. Pan and R.J. Plemmons, Analysis of a recursive least squares hyperbolic rotation algorithm for signal processing, Lin. Alg. Appl. 98(1988)3\u201340.","journal-title":"Lin. Alg. Appl."},{"key":"BF02071388_CR2","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/BF02145581","volume":"1","author":"D.L. Boley","year":"1991","unstructured":"D.L. Boley, S. Elhay, G.H. Golub and M.H. Gutknecht, Nonsymmetric Lanczos and finding orthogonal polynomials associated with indefinite weights, Numer. Algor. 1(1991)21\u201343.","journal-title":"Numer. Algor."},{"key":"BF02071388_CR3","doi-asserted-by":"crossref","first-page":"595","DOI":"10.1088\/0266-5611\/3\/4\/010","volume":"3","author":"D. Boley","year":"1987","unstructured":"D. Boley and G.H. Golub, A survey of matrix inverse eigenvalue problems, Inverse Problems 3(1987)595\u2013622.","journal-title":"Inverse Problems"},{"key":"BF02071388_CR4","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1016\/0024-3795(78)90086-1","volume":"21","author":"C. Boor de","year":"1978","unstructured":"C. de Boor and G.H. Golub, The numerically stable reconstruction of a Jacobi matrix from spectral data, Lin. Alg. Appl. 21(1978)245\u2013260.","journal-title":"Lin. Alg. Appl."},{"key":"BF02071388_CR5","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1016\/S0304-0208(08)72647-1","volume-title":"Large-Scale Eigenvalue Problems","author":"J. Cullum","year":"1986","unstructured":"J. Cullum and R.A. Willoughby, A practical procedure for computing eigenvalues of large sparse nonsymmetric matrices, in:Large-Scale Eigenvalue Problems, ed. J. Cullum and R.A. Willoughby (Elsevier, New York, 1986) pp. 193\u2013240."},{"key":"BF02071388_CR6","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1137\/0612024","volume":"12","author":"S. Elhay","year":"1991","unstructured":"S. Elhay, G.H. Golub and J. Kautsky, Updating and downdating of orthogonal polynomials with data-fitting applications, SIAM J. Matrix Anal. Appl. 12(1991)327\u2013353.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"BF02071388_CR7","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1090\/S0025-5718-1989-0972369-4","volume":"53","author":"\u00d6. Egecioglu","year":"1989","unstructured":"\u00d6. Egecioglu and \u00c7.K. Ko\u00e7, A fast algorithm for rational interpolation via orthogonal polynomials, Math. Comput. 53(1989)249\u2013264.","journal-title":"Math. Comput."},{"key":"BF02071388_CR8","doi-asserted-by":"crossref","first-page":"74","DOI":"10.1137\/0105007","volume":"5","author":"G.E. Forsythe","year":"1957","unstructured":"G.E. Forsythe, Generation and use of orthogonal polynomials for data-fitting with a digital computer, J. Soc. Ind. Appl. Math. 5(1957)74\u201388.","journal-title":"J. Soc. Ind. Appl. Math."},{"key":"BF02071388_CR9","doi-asserted-by":"crossref","first-page":"289","DOI":"10.1137\/0903018","volume":"3","author":"W. Gautschi","year":"1982","unstructured":"W. Gautschi, On generating orthogonal polynomials, SIAM J. Sci. Stat. Comput. 3(1982)289\u2013317.","journal-title":"SIAM J. Sci. Stat. Comput."},{"key":"BF02071388_CR10","doi-asserted-by":"crossref","first-page":"61","DOI":"10.1016\/0377-0427(85)90007-X","volume":"12 and 13","author":"W. Gautschi","year":"1985","unstructured":"W. Gautschi, Orthogonal polynomials \u2014 constructive theory and applications, J. Comput. Appl. Math. 12 and 13(1985)61\u201376.","journal-title":"J. Comput. Appl. Math."},{"key":"BF02071388_CR11","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1007\/978-1-4612-3704-4_5","volume-title":"Computation and Control","author":"W. Gautschi","year":"1989","unstructured":"W. Gautschi, Orthogonality \u2014 conventional and unconventional \u2014 in numerical analysis, in:Computation and Control, ed. K. Bowers and J. Lund (Birkh\u00e4user, Boston, 1989) pp. 63\u201395."},{"key":"BF02071388_CR12","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1007\/978-94-009-0501-6_9","volume-title":"Orthogonal Polynomials; Theory and Practice","author":"W. Gautschi","year":"1990","unstructured":"W. Gautschi, Computational aspects of orthogonal polynomials, in:Orthogonal Polynomials; Theory and Practice, ed. P. Nevai (Kluwer, Dordrecht, 1990) pp. 181\u2013216."},{"key":"BF02071388_CR13","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1016\/B978-0-12-498150-8.50021-5","volume-title":"Statistical Computation","author":"G.H. Golub","year":"1969","unstructured":"G.H. Golub, Matrix decompositions and statistical calculations, in:Statistical Computation, ed. R.C. Milton and J.A. Nelder (Academic Press, New York, 1969) pp. 365\u2013395."},{"key":"BF02071388_CR14","doi-asserted-by":"crossref","first-page":"607","DOI":"10.1007\/BF01386431","volume":"57","author":"G.H. Golub","year":"1990","unstructured":"G.H. Golub and M.H. Gutknecht, Modified moments for indefinite weight functions, Numer. Math. 57(1990)607\u2013624.","journal-title":"Numer. Math."},{"key":"BF02071388_CR15","volume-title":"Matrix Computations","author":"G.H. Golub","year":"1989","unstructured":"G.H. Golub and C.F. Van Loan,Matrix Computations, 2nd Ed. (Johns Hopkins, Baltimore, 1989).","edition":"2nd Ed."},{"key":"BF02071388_CR16","doi-asserted-by":"crossref","first-page":"213","DOI":"10.1216\/RMJ-1974-4-2-213","volume":"4","author":"W.B. Gragg","year":"1974","unstructured":"W.B. Gragg, Matrix interpretations and applications of the continued fraction algorithm, Rocky Mountain J. Math. 4(1974)213\u2013225.","journal-title":"Rocky Mountain J. Math."},{"key":"BF02071388_CR17","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/BF01405565","volume":"44","author":"W.B. Gragg","year":"1984","unstructured":"W.B. Gragg and W.J. Harrod, The numerically stable reconstruction of Jacobi matrices from spectral data, Numer. Math. 44(1984)317\u2013335.","journal-title":"Numer. Math."},{"key":"BF02071388_CR18","doi-asserted-by":"crossref","first-page":"552","DOI":"10.1137\/0612041","volume":"12","author":"L. Reichel","year":"1991","unstructured":"L. Reichel, Fast QR decomposition of Vandermonde-like matrices and polynomial least squares approximation, SIAM J. Matrix Anal. Appl. 12(1991)552\u2013564.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"BF02071388_CR19","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1090\/S0025-5718-1991-1079030-8","volume":"57","author":"L. Reichel","year":"1991","unstructured":"L. Reichel, G.S. Ammar and W.B. Gragg, Discrete least squares approximation by trigomometric polynomials, Math. Comput. 57(1991)273\u2013289.","journal-title":"Math. Comput."},{"key":"BF02071388_CR20","series-title":"Proc. Symp. Appl. Math.","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1090\/psapm\/015\/0160321","volume-title":"Experimental Arithmetic, High-Speed Computing and Mathematics","author":"H. Rutishauser","year":"1963","unstructured":"H. Rutishauser, On Jacobi rotation patterns, in:Experimental Arithmetic, High-Speed Computing and Mathematics, Proc. Symp. Appl. Math. 15 (Amer. Math. Soc., Providence, 1963) pp. 219\u2013239."},{"key":"BF02071388_CR21","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1145\/355826.355828","volume":"5","author":"L. Schrage","year":"1979","unstructured":"L. Schrage, A more portableFortran random number generator, ACM Trans. Math. Software 5(1979)132\u2013138.","journal-title":"ACM Trans. Math. Software"},{"key":"BF02071388_CR22","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/BF01385881","volume":"5","author":"G. Struble","year":"1963","unstructured":"G. Struble, Orthogonal polynomials: Variable-signed weight functions, Numer. Math. 5(1963)88\u201394.","journal-title":"Numer. Math."}],"container-title":["Advances in Computational Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02071388.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02071388\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02071388","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T00:06:34Z","timestamp":1557792394000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02071388"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,6]]},"references-count":22,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1993,6]]}},"alternative-id":["BF02071388"],"URL":"https:\/\/doi.org\/10.1007\/bf02071388","relation":{},"ISSN":["1019-7168","1572-9044"],"issn-type":[{"value":"1019-7168","type":"print"},{"value":"1572-9044","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,6]]}}}