{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,18]],"date-time":"2026-03-18T06:27:17Z","timestamp":1773815237887,"version":"3.50.1"},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[1996,12,1]],"date-time":"1996-12-01T00:00:00Z","timestamp":849398400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer Algor"],"published-print":{"date-parts":[[1996,12]]},"DOI":"10.1007\/bf02142505","type":"journal-article","created":{"date-parts":[[2005,10,29]],"date-time":"2005-10-29T06:53:20Z","timestamp":1130568800000},"page":"327-337","source":"Crossref","is-referenced-by-count":12,"title":["An algebraic approach to the vector \u03b5-algorithm"],"prefix":"10.1007","volume":"11","author":[{"given":"A.","family":"Salam","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"BF02142505_CR1","volume-title":"Determinants and Matrices","author":"A.C. Aitken","year":"1965","unstructured":"A.C. Aitken,Determinants and Matrices (Oliver and Boyd, Edinburgh, 1965)."},{"key":"BF02142505_CR2","volume-title":"Geometric Algebra","author":"A. Artin","year":"1966","unstructured":"A. Artin,Geometric Algebra (Interscience, New York, 1966)."},{"key":"BF02142505_CR3","volume-title":"Extrapolation Methods. Theory and Practice","author":"C. Brezinski","year":"1991","unstructured":"C. Brezinski and M. Redivo-Zaglia,Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1991)."},{"key":"BF02142505_CR4","doi-asserted-by":"crossref","first-page":"175","DOI":"10.1007\/BF01396314","volume":"35","author":"C. Brezinski","year":"1980","unstructured":"C. Brezinski, A general extrapolation algorithm, Numer. Math. 35 (1980) 175\u2013187.","journal-title":"Numer. Math."},{"key":"BF02142505_CR5","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0024-3795(74)90010-X","volume":"8","author":"C. Brezinski","year":"1974","unstructured":"C. Brezinski, Some results in the theory of the vector \u03b5-algorithm, Lin. Alg. Appl. 8 (1974) 77\u201386.","journal-title":"Lin. Alg. Appl."},{"key":"BF02142505_CR6","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/0024-3795(75)90113-5","volume":"11","author":"C. Brezinski","year":"1975","unstructured":"C. Brezinski, Computation of the eigenelements of a matrix by the \u03b5-algorithm, Lin. Alg. Appl. 11 (1975) 7\u201320.","journal-title":"Lin. Alg. Appl."},{"key":"BF02142505_CR7","first-page":"1174","volume":"271A","author":"C. Brezinski","year":"1970","unstructured":"C. Brezinski, Application de l'\u03b5-algorithme \u00e0 la r\u00e9solution des syst\u00e8mes non lin\u00e9aires, C.R. Acad. Sci. Paris 271A 1970) 1174\u20131177.","journal-title":"C.R. Acad. Sci. Paris"},{"key":"BF02142505_CR8","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1007\/BF02521609","volume":"2","author":"C. Brezinski","year":"1994","unstructured":"C. Brezinski and M. Redivo-Zaglia, A general extrapolation procedure revisited, Adv. Comp. Math. 2 (1994) 461\u2013477.","journal-title":"Adv. Comp. Math."},{"key":"BF02142505_CR9","doi-asserted-by":"crossref","unstructured":"C. Brezinski and A. Salam, Matrix and vector sequence transformations revisited, Proc. Edinb. Math. Soc., to appear.","DOI":"10.1017\/S0013091500019295"},{"key":"BF02142505_CR10","volume-title":"Formes Quadratiques et Groupes Classiques","author":"R. Deheuvels","year":"1981","unstructured":"R. Deheuvels,Formes Quadratiques et Groupes Classiques (Presses Universitaires de France, Paris, 1981)."},{"key":"BF02142505_CR11","volume-title":"La G\u00e9om\u00e9trie des Groupes Classiques","author":"J. Dieudonn\u00e9","year":"1952","unstructured":"J. Dieudonn\u00e9,La G\u00e9om\u00e9trie des Groupes Classiques (Springer, Berlin, 1952)."},{"key":"BF02142505_CR12","doi-asserted-by":"crossref","first-page":"427","DOI":"10.1090\/S0025-5718-1972-0314226-X","volume":"26","author":"E. Gekeler","year":"1972","unstructured":"E. Gekeler, On the solution of systems of equations by the epsilon algorithm of Wynn, Math. Comp. 26 (1972) 427\u2013436.","journal-title":"Math. Comp."},{"key":"BF02142505_CR13","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF01389578","volume":"42","author":"P.R. Graves-Morris","year":"1983","unstructured":"P.R. Graves-Morris, Vector-valued rational interpolants I, Numer. Math. 42 (1983) 331\u2013348.","journal-title":"Numer. Math."},{"key":"BF02142505_CR14","doi-asserted-by":"crossref","unstructured":"P.R. Graves-Morris and D.E. Roberts, From matrix to vector Pad\u00e9 approximants, J. Comp. Appl. Math., to appear.","DOI":"10.1016\/0377-0427(92)00008-W"},{"key":"BF02142505_CR15","doi-asserted-by":"crossref","first-page":"204","DOI":"10.1007\/BF01930850","volume":"19","author":"T. Havie","year":"1979","unstructured":"T. Havie, Generalized Neville type extrapolation schemes, BIT 19 (1979) 204\u2013213.","journal-title":"BIT"},{"key":"BF02142505_CR16","doi-asserted-by":"crossref","first-page":"465","DOI":"10.1007\/BF01451604","volume":"98","author":"A. Heyting","year":"1927","unstructured":"A. Heyting, Die Theorie der linearen Gleichungen in einer Zahlenspezies mit nichtkommutativer Multiplikation, Math. Ann. 98 (1927) 465\u2013490.","journal-title":"Math. Ann."},{"key":"BF02142505_CR17","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0024-3795(90)90282-H","volume":"128","author":"G.N. Hile","year":"1990","unstructured":"G.N. Hile and P. Lounesto, Matrix representations of Clifford algebras, Lin. Alg. Appl. 128 (1990) 51\u201363.","journal-title":"Lin. Alg. Appl."},{"key":"BF02142505_CR18","doi-asserted-by":"crossref","first-page":"406","DOI":"10.1017\/S0305004100030401","volume":"51","author":"R. Penrose","year":"1955","unstructured":"R. Penrose, A generalised inverse for matrices, Proc. Cambridge Phil. Soc. 51 (1955) 406\u2013413.","journal-title":"Proc. Cambridge Phil. Soc."},{"key":"BF02142505_CR19","unstructured":"A. Salam, Extrapolation: Extension et nouveaux r\u00e9sultats, Thesis, Universit\u00e9 des Sciences et Technologies de Lille (1993)."},{"key":"BF02142505_CR20","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF02140685","volume":"7","author":"A. Salam","year":"1994","unstructured":"A. Salam, Non-commutative extrapolation algorithms, Numer. Algor. 7 (1994) 225\u2013251.","journal-title":"Numer. Algor."},{"key":"BF02142505_CR21","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1007\/978-94-011-0970-3_25","volume-title":"Nonlinear Numerical Methods and Rational Approximation II","author":"A. Salam","year":"1994","unstructured":"A. Salam, On the vector-valued Pad\u00e9 approximants and the vector \u03b5-algorithm, in:Nonlinear Numerical Methods and Rational Approximation II ed. A. Cuyt (Kluwer, Dordrecht, 1994) pp. 291\u2013301."},{"key":"BF02142505_CR22","unstructured":"A. Salam, What is a vector Hankel determinant, to appear."},{"key":"BF02142505_CR23","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/sapm19553411","volume":"34","author":"D. Shanks","year":"1955","unstructured":"D. Shanks, Nonlinear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955) 1\u201342.","journal-title":"J. Math. Phys."},{"issue":"2","key":"BF02142505_CR24","first-page":"13","volume":"25","author":"I.M. Gel'fand","year":"1991","unstructured":"I.M. Gel'fand and V.S. Retakh, Determinants of matrices over noncommutative rings, Funktsional\u0144yi Analiz i Ego Prilozheniya 25 (1991) 2, 13\u201325.","journal-title":"Funktsional\u0144yi Analiz i Ego Prilozheniya"},{"key":"BF02142505_CR25","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1016\/0167-7977(89)90011-7","volume":"10","author":"E.J. Weniger","year":"1989","unstructured":"E.J. Weniger, Nonlinear sequence transformations for the acceleration of convergence and the summation of divergent series, Comp. Phys. Rep. 10 (1989) 189\u2013371.","journal-title":"Comp. Phys. Rep."},{"key":"BF02142505_CR26","first-page":"91","volume":"10","author":"P. Wynn","year":"1956","unstructured":"P. Wynn, On a device for computing thee m (S n ) transformation, MTAC 10 (1956) 91\u201396.","journal-title":"MTAC"},{"key":"BF02142505_CR27","doi-asserted-by":"crossref","first-page":"357","DOI":"10.1016\/0024-3795(68)90015-3","volume":"1","author":"P. Wynn","year":"1968","unstructured":"P. Wynn, Vector continued fractions, Lin. Alg. Appl. 1 (1968) 357\u2013395.","journal-title":"Lin. Alg. Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02142505.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/BF02142505\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BF02142505","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,14]],"date-time":"2019-05-14T09:45:03Z","timestamp":1557827103000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BF02142505"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1996,12]]},"references-count":27,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1996,12]]}},"alternative-id":["BF02142505"],"URL":"https:\/\/doi.org\/10.1007\/bf02142505","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1996,12]]}}}