{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,24]],"date-time":"2025-08-24T01:18:55Z","timestamp":1755998335010,"version":"3.41.2"},"reference-count":40,"publisher":"Springer Science and Business Media LLC","issue":"1-3","license":[{"start":{"date-parts":[[2002,3,1]],"date-time":"2002-03-01T00:00:00Z","timestamp":1014940800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2002,3,1]],"date-time":"2002-03-01T00:00:00Z","timestamp":1014940800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numerical Algorithms"],"published-print":{"date-parts":[[2002,3]]},"DOI":"10.1023\/a:1014832627766","type":"journal-article","created":{"date-parts":[[2002,12,29]],"date-time":"2002-12-29T19:13:07Z","timestamp":1041189187000},"page":"229-247","source":"Crossref","is-referenced-by-count":7,"title":["On the Vector \u03b5-Algorithm for Solving Linear Systems of Equations"],"prefix":"10.1007","volume":"29","author":[{"given":"A.","family":"Salam","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.R.","family":"Graves-Morris","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"395861_CR1","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1090\/qam\/42792","volume":"9","author":"W.E. Arnoldi","year":"1951","unstructured":"W.E. Arnoldi, The principle of minimized iterations in the solution of the matrix eigenvalue problem, Quart. Appl. Math. 9 (1951) 17\u201329.","journal-title":"Quart. Appl. Math."},{"key":"395861_CR2","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/0024-3795(80)90226-8","volume":"29","author":"O. Axelsson","year":"1980","unstructured":"O. Axelsson, Conjugate gradient type methods for unsymmetric and inconsistent systems of linear equations, Linear Algebra Appl. 29 (1980) 1\u201316.","journal-title":"Linear Algebra Appl."},{"key":"395861_CR3","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 e-algorithm, Linear Algebra Appl. 8 (1974) 77\u201386.","journal-title":"Linear Algebra Appl."},{"key":"395861_CR4","doi-asserted-by":"crossref","first-page":"317","DOI":"10.1007\/BF02575753","volume":"12","author":"C. Brezinski","year":"1975","unstructured":"C. Brezinski, G\u00e9n\u00e9ralisations de la transformation de Shanks, de la table de Pad\u00e9 et de l' e-algorithme, Calcolo 12 (1975) 317\u2013360.","journal-title":"Calcolo"},{"key":"395861_CR5","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-0348-6558-6","volume-title":"Pad\u00e9-Type Approximation and General Orthogonal Polynomials","author":"C. Brezinski","year":"1980","unstructured":"C. Brezinski, Pad\u00e9-Type Approximation and General Orthogonal Polynomials (Birkh\u00e4user, Basel, 1980)."},{"key":"395861_CR6","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/BF02141260","volume":"7","author":"C. Brezinski","year":"1994","unstructured":"C. Brezinski and M. Redivo-Zaglia, Treatment of near-breakdown in the CGS algorithms, Numer. Algorithms 7 (1994) 33\u201373.","journal-title":"Numer. Algorithms"},{"key":"395861_CR7","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1007\/BF01737161","volume":"35","author":"C. Brezinski","year":"1995","unstructured":"C. Brezinski and M. Redivo-Zaglia, Look-ahead in BiCGSTAB and other product-type methods for linear systems, BIT 35 (1995) 169\u2013201.","journal-title":"BIT"},{"key":"395861_CR8","volume-title":"Extrapolation Methods. Theory and Practice","author":"C. Brezinski","year":"1996","unstructured":"C. Brezinski and M. Redivo-Zaglia, Extrapolation Methods. Theory and Practice (North-Holland, Amsterdam, 1996)."},{"key":"395861_CR9","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1007\/BF02142321","volume":"1","author":"C. Brezinski","year":"1991","unstructured":"C. Brezinski and H. Sadok, Avoiding breakdown in the CGS algorithm, Numer. Algorithms 1 (1991) 199\u2013206.","journal-title":"Numer. Algorithms"},{"key":"395861_CR10","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1016\/0168-9274(93)90087-8","volume":"11","author":"C. Brezinski","year":"1993","unstructured":"C. Brezinski and H. Sadok, Lanczos-type algorithms for solving systems of linear equations, Appl. Numer. Math. 11 (1993) 443\u2013473.","journal-title":"Appl. Numer. Math."},{"key":"395861_CR11","doi-asserted-by":"crossref","first-page":"734","DOI":"10.1137\/0713060","volume":"13","author":"S. Cabay","year":"1976","unstructured":"S. Cabay and L.W. Jackson, A polynomial extrapolation method for finding limits and antilimits of vector sequences, SIAM J. Numer. Anal. 13 (1976) 734\u2013752.","journal-title":"SIAM J. Numer. Anal."},{"key":"395861_CR12","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1016\/B978-0-12-734250-4.50028-X","volume-title":"Information Linkage between Applied Mathematics and Industry","author":"R.P. Eddy","year":"1979","unstructured":"R.P. Eddy, Extrapolating to the limit of a vector sequence, in: Information Linkage between Applied Mathematics and Industry, ed. P.C.C. Wang (Academic Press, New York, 1979) pp. 387\u2013396."},{"key":"395861_CR13","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1137\/0720023","volume":"20","author":"S.C. Eisenstat","year":"1983","unstructured":"S.C. Eisenstat, H.C. Elman and M.H. Schultz, Variational iterative methods for nonsymmetric systems of linear equations, SIAM J. Numer. Anal. 20 (1983) 345\u2013357.","journal-title":"SIAM J. Numer. Anal."},{"key":"395861_CR14","series-title":"Computer Systems Science","first-page":"279","volume-title":"Supercomputing","author":"W. Gander","year":"1989","unstructured":"W. Gander, G.H. Golub and D. Gruntz, Solving linear equations by extrapolation, in: Supercomputing, Trondheim, 1989, Computer Systems Science, Vol. 62 (Springer, Berlin, 1989) pp. 279\u2013293."},{"key":"395861_CR15","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":"395861_CR16","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1093\/imanum\/4.2.209","volume":"4","author":"P.R. Graves-Morris","year":"1984","unstructured":"P.R. Graves-Morris, Vector valued rational interpolants II, IMA J. Numer. Anal. 4 (1984) 209\u2013224.","journal-title":"IMA J. Numer. Anal."},{"key":"395861_CR17","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0377-0427(95)00176-X","volume":"66","author":"P.R. Graves-Morris","year":"1996","unstructured":"P.R. Graves-Morris, G.A. Baker Jr. and C.F. Woodcock, Cayley's theorem and its application in the theory of vector Pad\u00e9 approximants, J. Comput. Appl. Math. 66 (1996) 255\u2013265.","journal-title":"J. Comput. Appl. Math."},{"key":"395861_CR18","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1007\/BF01893432","volume":"2","author":"P.R. Graves-Morris","year":"1986","unstructured":"P.R. Graves-Morris and C.D. Jenkins, Vector-valued, rational interpolants III, Constr. Approx. 2 (1986) 263\u2013289.","journal-title":"Constr. Approx."},{"key":"395861_CR19","first-page":"33","volume":"49","author":"C. Lanczos","year":"1952","unstructured":"C. Lanczos, Solution of systems of linear equations by minimized iteration, J. Res. N.B.S. 49 (1952) 33\u201353.","journal-title":"J. Res. N.B.S."},{"key":"395861_CR20","doi-asserted-by":"crossref","first-page":"17","DOI":"10.1007\/BF02279938","volume":"7","author":"J.B. McLeod","year":"1971","unstructured":"J.B. McLeod, A note on the e-algorithm, Computing 7 (1971) 17\u201324.","journal-title":"Computing"},{"key":"395861_CR21","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1016\/0045-7825(77)90004-4","volume":"10","author":"M. Mesina","year":"1977","unstructured":"M. Me\u0161ina, Convergence acceleration for the iterative solution of the equations X= AX+ f, Comput. Methods Appl. Mech. Engrg. 10 (1977) 165\u2013173.","journal-title":"Comput. Methods Appl. Mech. Engrg."},{"key":"395861_CR22","doi-asserted-by":"crossref","first-page":"147","DOI":"10.1016\/0022-247X(70)90126-5","volume":"31","author":"J. Nuttall","year":"1970","unstructured":"J. Nuttall, Convergence of Pad\u00e9 approximants of meromorphic functions, J. Math. Anal. Appl. 31 (1970) 147\u2013153.","journal-title":"J. Math. Anal. Appl."},{"key":"395861_CR23","doi-asserted-by":"crossref","first-page":"285","DOI":"10.1098\/rspa.1990.0131","volume":"431","author":"D.E. Roberts","year":"1990","unstructured":"D.E. Roberts, Clifford algebras and vector-valued rational forms I, Proc. Roy. Soc. London A 431 (1990) 285\u2013300.","journal-title":"Proc. Roy. Soc. London A"},{"key":"395861_CR24","doi-asserted-by":"crossref","first-page":"371","DOI":"10.1007\/BF02141944","volume":"3","author":"D.E. Roberts","year":"1992","unstructured":"D.E. Roberts, Clifford algebras and vector-valued rational forms II, Numer. Algorithms 3 (1992) 371\u2013381.","journal-title":"Numer. Algorithms"},{"key":"395861_CR25","doi-asserted-by":"crossref","first-page":"193","DOI":"10.1023\/A:1018944213562","volume":"8","author":"D.E. Roberts","year":"1998","unstructured":"D.E. Roberts, On a q-d algorithm, Adv. Comput. Math. 8 (1998) 193\u2013219.","journal-title":"Adv. Comput. Math."},{"key":"395861_CR26","doi-asserted-by":"crossref","first-page":"105","DOI":"10.1090\/S0025-5718-1981-0616364-6","volume":"37","author":"Y. Saad","year":"1981","unstructured":"Y. Saad, Krylov subspace methods for solving large unsymmetric linear systems, Math. Comp. 37 (1981) 105\u2013126.","journal-title":"Math. Comp."},{"key":"395861_CR27","volume-title":"Iterative Methods for Sparse Linear Systems","author":"Y. Saad","year":"1996","unstructured":"Y. Saad, Iterative Methods for Sparse Linear Systems (PWS, Boston, 1996)."},{"key":"395861_CR28","doi-asserted-by":"crossref","first-page":"267","DOI":"10.1023\/A:1018952415379","volume":"8","author":"A. Salam","year":"1988","unstructured":"A. Salam, Formal vector orthogonal polynomials, Adv. Comput. Math. 8 (1988) 267\u2013289.","journal-title":"Adv. Comput. Math."},{"key":"395861_CR29","doi-asserted-by":"crossref","first-page":"92","DOI":"10.1006\/jath.1997.3263","volume":"97","author":"A. Salam","year":"1999","unstructured":"A. Salam, Vector Pad\u00e9-type approximants and vector Pad\u00e9 approximants, J. Approx. Theory 97 (1999) 92\u2013112.","journal-title":"J. Approx. Theory"},{"key":"395861_CR30","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/S0024-3795(00)00102-6","volume":"313","author":"A. Salam","year":"2000","unstructured":"A. Salam, On vector Hankel determinant, Linear Algebra Appl. 313 (2000) 127\u2013139.","journal-title":"Linear Algebra Appl."},{"key":"395861_CR31","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1002\/sapm19553411","volume":"34","author":"D. Shanks","year":"1955","unstructured":"D. Shanks, Non-linear transformations of divergent and slowly convergent sequences, J. Math. Phys. 34 (1955) 1\u201342.","journal-title":"J. Math. Phys."},{"key":"395861_CR32","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1137\/0723014","volume":"23","author":"A. Sidi","year":"1986","unstructured":"A. Sidi, Convergence and stability properties of minimal polynomial and reduced rank extrapolation algorithms, SIAM J. Numer. Anal. 23 (1986) 197\u2013209.","journal-title":"SIAM J. Numer. Anal."},{"key":"395861_CR33","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1016\/0377-0427(88)90289-0","volume":"22","author":"A. Sidi","year":"1988","unstructured":"A. Sidi, Extrapolation vs. projection methods for linear systems of equations, J. Comput. Appl. Math. 22 (1988) 71\u201388.","journal-title":"J. Comput. Appl. Math."},{"key":"395861_CR34","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1137\/0723013","volume":"23","author":"A. Sidi","year":"1986","unstructured":"A. Sidi, W.F. Ford and D.A. Smith, Acceleration of convergence of vectors sequences, SIAM J. Numer. Anal. 23 (1986) 178\u2013196.","journal-title":"SIAM J. Numer. Anal."},{"key":"395861_CR35","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1137\/0723013","volume":"23","author":"D.A. Smith","year":"1986","unstructured":"D.A. Smith, W.F. Ford and A. Sidi, Extrapolation methods for vector sequences, SIAM J. Numer Anal. 23 (1986) 178\u2013196.","journal-title":"SIAM J. Numer Anal."},{"key":"395861_CR36","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1137\/0910004","volume":"10","author":"P. Sonneveld","year":"1989","unstructured":"P. Sonneveld, CGS, A fast Lanczos-type solver for nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 10 (1989) 35\u201352.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"395861_CR37","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1137\/0913035","volume":"13","author":"H.A. Van Der Vorst","year":"1992","unstructured":"H.A. Van Der Vorst, BiCGSTAB: A fast and smoothly converging variant of the Bi-CG for the solution of nonsymmetric linear systems, SIAM J. Sci. Statist. Comput. 13 (1992) 631\u2013644.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"395861_CR38","doi-asserted-by":"crossref","first-page":"91","DOI":"10.2307\/2002183","volume":"10","author":"P. Wynn","year":"1956","unstructured":"P. Wynn, On a device for computing the e\nm\n(S\nn\n)transformation, Math. Tables Autom. Comp. 10 (1956) 91\u201396.","journal-title":"Math. Tables Autom. Comp."},{"key":"395861_CR39","doi-asserted-by":"crossref","first-page":"301","DOI":"10.1090\/S0025-5718-1962-0145647-X","volume":"16","author":"P. Wynn","year":"1962","unstructured":"P. Wynn, Acceleration techniques for iterated vector and matrix problems, Math. Comput. 16 (1962) 301\u2013322.","journal-title":"Math. Comput."},{"key":"395861_CR40","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, Linear Algebra Appl. 1 (1968) 357\u2013395.","journal-title":"Linear Algebra Appl."}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014832627766.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1014832627766\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1014832627766.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T07:22:12Z","timestamp":1751872932000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1014832627766"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":40,"journal-issue":{"issue":"1-3","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["395861"],"URL":"https:\/\/doi.org\/10.1023\/a:1014832627766","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"type":"print","value":"1017-1398"},{"type":"electronic","value":"1572-9265"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}