{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T09:18:50Z","timestamp":1777367930736,"version":"3.51.4"},"reference-count":65,"publisher":"Springer Science and Business Media LLC","issue":"2-3","license":[{"start":{"date-parts":[[1999,8,1]],"date-time":"1999-08-01T00:00:00Z","timestamp":933465600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[1999,8,1]],"date-time":"1999-08-01T00:00:00Z","timestamp":933465600000},"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":[[1999,8]]},"DOI":"10.1023\/a:1019112103049","type":"journal-article","created":{"date-parts":[[2003,2,19]],"date-time":"2003-02-19T23:30:27Z","timestamp":1045697427000},"page":"165-194","source":"Crossref","is-referenced-by-count":36,"title":["UTV Tools: Matlab templates for rank-revealing UTV decompositions"],"prefix":"10.1007","volume":"20","author":[{"given":"Ricardo D.","family":"Fierro","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Per Christian","family":"Hansen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter S\u00f8ren Kirk","family":"Hansen","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"329305_CR1","doi-asserted-by":"crossref","unstructured":"G. Adams, M.F. Griffin and G.W. Stewart, Direction-of-arrival estimation using the rank-revealing URV decomposition, in: Proc. of IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing, Washington (1991).","DOI":"10.1109\/ICASSP.1991.150681"},{"key":"329305_CR2","first-page":"117","volume-title":"Recent Advances in Total Least Squares Techniques and Errors-In-Variables Modeling","author":"J.L. Barlow","year":"1997","unstructured":"J.L. Barlow and P.A. Yoon, Solving recursive TLS problems using the rank-revealing ULV decomposition, in: Recent Advances in Total Least Squares Techniques and Errors-In-Variables Modeling, ed. S. Van Huffel (SIAM, Philadelphia, PA, 1997) pp. 117\u2013126."},{"key":"329305_CR3","doi-asserted-by":"publisher","first-page":"15","DOI":"10.1007\/BF01740542","volume":"36","author":"J.L. Barlow","year":"1996","unstructured":"J.L. Barlow, P.A. Yoon and H. Zha, An algorithm and a stability theory for downdating the ULV decomposition, BIT 36 (1996) 15\u201340.","journal-title":"BIT"},{"key":"329305_CR4","doi-asserted-by":"publisher","first-page":"573","DOI":"10.1137\/1037127","volume":"37","author":"M.W. Berry","year":"1995","unstructured":"M.W. Berry, S.T. Dumais and G.W. O'Brien, Using linear algebra for intelligent information retrieval, SIAM Rev. 37 (1995) 573\u2013595.","journal-title":"SIAM Rev."},{"key":"329305_CR5","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1016\/0165-1684(89)90039-X","volume":"18","author":"E. Biglieri","year":"1989","unstructured":"E. Biglieri and K. Yao, Some properties of singular value decomposition and their applications to digital signal processing, Signal Processing 18 (1989) 277\u2013289.","journal-title":"Signal Processing"},{"key":"329305_CR6","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1109\/78.157185","volume":"40","author":"C.H. Bischof","year":"1992","unstructured":"C.H. Bischof and G.M. Shroff, On updating signal subspaces, IEEE Trans. Signal Processing 40 (1992) 96\u2013105.","journal-title":"IEEE Trans. Signal Processing"},{"key":"329305_CR7","doi-asserted-by":"publisher","first-page":"549","DOI":"10.1137\/S089547989222895X","volume":"15","author":"\u00c5. Bj\u00f6rck","year":"1994","unstructured":"\u00c5. Bj\u00f6rck, H. Park and L. Eld\u00e9n, Accurate downdating of least squares solutions, SIAM J. Matrix Anal. Appl. 15 (1994) 549\u2013568.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR8","volume-title":"Applied Linear Algebra","author":"A.W. Bojanczyk","year":"1994","unstructured":"A.W. Bojanczyk and J.M. Lebak, Downdating a ULLV decomposition of two matrices; in: Applied Linear Algebra, ed. J.G. Lewis (SIAM, Philadelphia, PA, 1994)."},{"key":"329305_CR9","doi-asserted-by":"publisher","first-page":"111","DOI":"10.1007\/BF01397471","volume":"31","author":"J.R. Bunch","year":"1978","unstructured":"J.R. Bunch and N.P. Nielsen, Updating the singular value decomposition, Numer. Math. 31 (1978) 111\u2013129.","journal-title":"Numer. Math."},{"key":"329305_CR10","doi-asserted-by":"publisher","first-page":"67","DOI":"10.1016\/0024-3795(87)90103-0","volume":"88","author":"T.F. Chan","year":"1987","unstructured":"T.F. Chan, Rank revealing QR factorizations, Linear Algebra Appl. 88\/89 (1987) 67\u201382.","journal-title":"Linear Algebra Appl."},{"key":"329305_CR11","doi-asserted-by":"publisher","first-page":"727","DOI":"10.1137\/0913043","volume":"13","author":"T.F. Chan","year":"1992","unstructured":"T.F. Chan and P.C. Hansen, Some applications of the rank revealing QR factorization, SIAM J. Sci. Statist. Comput. 13 (1992) 727\u2013741.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"329305_CR12","doi-asserted-by":"publisher","first-page":"33","DOI":"10.1002\/nla.1680010105","volume":"1","author":"T.F. Chan","year":"1994","unstructured":"T.F. Chan and P.C. Hansen, Low-rank revealing QR factorizations, Numer. Linear Algebra Appl. 1 (1994) 33\u201344.","journal-title":"Numer. Linear Algebra Appl."},{"key":"329305_CR13","series-title":"Lecture Notes in Mathematics","volume-title":"Numerical Analysis","author":"A.K. Cline","year":"1882","unstructured":"A.K. Cline, A.R. Conn and C.F. Van Loan, Generalizing the LINPACK condition estimator, in: Numerical Analysis, ed. J.P. Hennart, Lecture Notes in Mathematics, Vol. 909 (Springer, Berlin, 1882)."},{"key":"329305_CR14","doi-asserted-by":"publisher","first-page":"1337","DOI":"10.1109\/5.58320","volume":"78","author":"P. Comon","year":"1990","unstructured":"P. Comon and G.H. Golub, Tracking a few extreme singular values and vectors in signal processing, Proc. IEEE 78 (1990) 1337\u20131343.","journal-title":"Proc. IEEE"},{"key":"329305_CR15","doi-asserted-by":"publisher","first-page":"772","DOI":"10.2307\/2005398","volume":"30","author":"J.W. Daniel","year":"1976","unstructured":"J.W. Daniel, W.B. Gragg, L. Kaufman and G.W. Stewart, Reorthogonalization and stable algorithms for updating the Gram\u2013Schmidt QR factorization, Math. Comp. 30 (1976) 772\u2013795.","journal-title":"Math. Comp."},{"key":"329305_CR16","unstructured":"B. De Moor, Generalizations of the OSVD: Structure, properties and applications, in: [59] pp. 83\u201398."},{"key":"329305_CR17","volume-title":"SVD and Signal Processing, Algorithms, Applications, and Architectures","author":"F. Deprettere","year":"1988","unstructured":"F. Deprettere, SVD and Signal Processing, Algorithms, Applications, and Architectures (North-Holland, Amsterdam, 1988)."},{"key":"329305_CR18","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1016\/0165-1684(96)00009-6","volume":"50","author":"L. Eld\u00e9n","year":"1996","unstructured":"L. Eld\u00e9n and E. Sj\u00f6str\u00f6m, Fast computation of the principal singular vectors of Toeplitz matrices arising in exponential data modelling, Signal Processing 50 (1996) 151\u2013164.","journal-title":"Signal Processing"},{"key":"329305_CR19","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1137\/S0895479894264491","volume":"17","author":"R.D. Fierro","year":"1996","unstructured":"R.D. Fierro, Perturbation analysis for two-sided (or complete) orthogonal decompositions, SIAM J. Matrix Anal. Appl. 17 (1996) 383\u2013400.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR20","doi-asserted-by":"publisher","first-page":"743","DOI":"10.1137\/S0895479893246005","volume":"16","author":"R.D. Fierro","year":"1995","unstructured":"R.D. Fierro and J.R. Bunch, Bounding the subspaces from rank revealing two-sided orthogonal decompositions, SIAM J. Matrix Anal. Appl. 16 (1995) 743\u2013759.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR21","doi-asserted-by":"publisher","first-page":"453","DOI":"10.1007\/s002110050128","volume":"70","author":"R.D. Fierro","year":"1995","unstructured":"R.D. Fierro and P.C. Hansen, Accuracy of TSVD solutions computed from rank-revealing decompositions, Numer. Math. 70 (1995) 453\u2013471.","journal-title":"Numer. Math."},{"key":"329305_CR22","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1023\/A:1019254318361","volume":"15","author":"R.D. Fierro","year":"1997","unstructured":"R.D. Fierro and P.C. Hansen, Low-rank revealing UTV decompositions, Numerical Algorithms 15 (1997) 37\u201355.","journal-title":"Numerical Algorithms"},{"key":"329305_CR23","first-page":"99","volume-title":"Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling","author":"R.D. Fierro","year":"1997","unstructured":"R.D. Fierro, L. Vanhamme and S. Van Huffel, Total least squares algorithms based on rank-revealing complete orthogonal decompositions, in: Recent Advances in Total Least Squares Techniques and Errors-in-Variables Modeling, ed. S. Van Huffel (SIAM, Philadelphia, PA, 1997) pp. 99\u2013116."},{"key":"329305_CR24","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1016\/0024-3795(86)90115-1","volume":"74","author":"L. Foster","year":"1986","unstructured":"L. Foster, Rank and null space calculations using matrix decomposition without column interchanges, Linear Algebra Appl. 74 (1986) 47\u201371.","journal-title":"Linear Algebra Appl."},{"key":"329305_CR25","series-title":"Technical Report","volume-title":"Rank degeneracy and least squares problems","author":"G.H. Golub","year":"1976","unstructured":"G.H. Golub, V. Klema and G.W. Stewart, Rank degeneracy and least squares problems, Technical Report TR-456, Dept. of Computer Science, University of Maryland, MD (1976)."},{"key":"329305_CR26","volume-title":"Matrix Computations","author":"G.H. Golub","year":"1996","unstructured":"G.H. Golub and C.F. Van Loan, Matrix Computations, 3rd ed. (Johns Hopkins University Press, Baltimore, MD, 1996).","edition":"3rd ed."},{"key":"329305_CR27","doi-asserted-by":"publisher","first-page":"793","DOI":"10.1137\/S0895479893251472","volume":"16","author":"M. Gu","year":"1995","unstructured":"M. Gu and S.C. Eisenstat, Downdating the singular value decomposition, SIAM J. Matrix Anal. Appl. 16 (1995) 793\u2013810.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR28","doi-asserted-by":"publisher","first-page":"117","DOI":"10.1016\/0377-0427(88)90336-6","volume":"23","author":"P.C. Hansen","year":"1988","unstructured":"P.C. Hansen, The 2-norm of random matrices, J. Comput. Appl. Math. 23 (1988) 117\u2013120.","journal-title":"J. Comput. Appl. Math."},{"key":"329305_CR29","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898719697","volume-title":"Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion","author":"P.C. Hansen","year":"1998","unstructured":"P.C. Hansen, Rank-Deficient and Discrete Ill-Posed Problems: Numerical Aspects of Linear Inversion (SIAM, Philadelphia, PA, 1998)."},{"key":"329305_CR30","doi-asserted-by":"crossref","first-page":"34","DOI":"10.1007\/BF02510915","volume":"38","author":"P.C. Hansen","year":"1998","unstructured":"P.C. Hansen, Rank-deficient prewhitening by quotient SVD and UTV, BIT 38 (1998) 34\u201343.","journal-title":"BIT"},{"key":"329305_CR31","unstructured":"P.S.K. Hansen, Signal subspace methods for speech enhancement, Ph.D. thesis, Dept. of Mathematical Modelling, Technical University of Denmark (1997)."},{"key":"329305_CR32","doi-asserted-by":"publisher","first-page":"575","DOI":"10.1137\/1029112","volume":"29","author":"N.J. Higham","year":"1987","unstructured":"N.J. Higham, A survey of condition number estimation for triangular matrices, SIAM Rev. 29 (1987) 575\u2013596.","journal-title":"SIAM Rev."},{"key":"329305_CR33","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1109\/89.482211","volume":"3","author":"S.H. Jensen","year":"1995","unstructured":"S.H. Jensen, P.C. Hansen, S.D. Hansen and J.A. S\u00f8rensen, Reduction of broad-band noise in speech by truncated QSVD, IEEE Trans. Audio Speech Proc. 3 (1995) 439\u2013448.","journal-title":"IEEE Trans. Audio Speech Proc."},{"key":"329305_CR34","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1137\/0613066","volume":"4","author":"J. Kuczynski","year":"1992","unstructured":"J. Kuczynski and H. Wozniakowski, Estimating the largest eigenvalue by the Power and Lanczos algorithms with a random start, SIAM J. Matrix Anal. 4 (1992) 1094\u20131122.","journal-title":"SIAM J. Matrix Anal."},{"key":"329305_CR35","volume-title":"Solving Least Squares Problems","author":"C.L. Lawson","year":"1974","unstructured":"C.L. Lawson and R.J. Hanson, Solving Least Squares Problems (Prentice-Hall, Englewood Cliffs, NJ, 1974). Reprinted by SIAM, Philadelphia."},{"key":"329305_CR36","unstructured":"J.M. Lebak and A.W. Bojanczyk, Modifying a rank-revealing ULLV decomposition, Manuscript, School of Electrical Engineering, Cornell University (1994)."},{"key":"329305_CR37","doi-asserted-by":"publisher","first-page":"3441","DOI":"10.1109\/78.340778","volume":"42","author":"K.J.R. Liu","year":"1994","unstructured":"K.J.R. Liu, D.P. O'Leary, G.W. Stewart and Y.-J. Wu, URV ESPRIT for tracking time-varying signals, IEEE Trans. Signal Processing 42 (1994) 3441\u20133448.","journal-title":"IEEE Trans. Signal Processing"},{"key":"329305_CR38","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1016\/0005-1098(94)90227-5","volume":"30","author":"F.T. Luk","year":"1994","unstructured":"F.T. Luk and S. Qiao, A new matrix decomposition for signal processing, Automatica 30 (1994) 39\u201343.","journal-title":"Automatica"},{"key":"329305_CR39","doi-asserted-by":"crossref","unstructured":"F.T. Luk and S. Qiao, An adaptive algorithm for interference cancelling in array processing, in: Advanced Signal Processing Algorithms, Architectures, and Implementations VI, ed. F.T. Luk, SPIE Proceedings, Vol. 2846 (1996) pp. 151\u2013161.","DOI":"10.1117\/12.255429"},{"key":"329305_CR40","volume-title":"Curves and Surfaces in Geometric Design","author":"W. Ma","year":"1994","unstructured":"W. Ma and J.P. Kruth, Mathematical modelling of free-form curves and surfaces from discrete points with NURBS, in: Curves and Surfaces in Geometric Design, eds. P.J. Laurent, A. Le M\u00e9haut\u00e9 and L.L Schumaker (A.K. Peters, Wellesley, MA, 1994)."},{"key":"329305_CR41","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1016\/0024-3795(93)90493-8","volume":"182","author":"R. Mathias","year":"1993","unstructured":"R. Mathias and G.W. Stewart, A block QR algorithm and the singular value decomposition, Linear Algebra Appl. 182 (1993) 91\u2013100.","journal-title":"Linear Algebra Appl."},{"key":"329305_CR42","volume-title":"SVD and Signal Processing, III, Algorithms, Architectures and Applications","author":"M. Moonen","year":"1995","unstructured":"M. Moonen and B. De Moor, SVD and Signal Processing, III, Algorithms, Architectures and Applications (Elsevier, Amsterdam, 1995)."},{"key":"329305_CR43","doi-asserted-by":"publisher","first-page":"1911","DOI":"10.1109\/78.91165","volume":"39","author":"M. Moonen","year":"1991","unstructured":"M. Moonen, P. Van Dooren and J. Vandewalle, A note on efficient numerically stabilized rank-one eigenstructure updating, IEEE Trans. Signal Processing 39 (1991) 1911\u20131913.","journal-title":"IEEE Trans. Signal Processing"},{"key":"329305_CR44","doi-asserted-by":"publisher","first-page":"1015","DOI":"10.1137\/0613061","volume":"13","author":"M. Moonen","year":"1992","unstructured":"M. Moonen, P. Van Dooren and J. Vandewalle, A singular value decomposition updating algorithm for subspace tracking, SIAM J. Matrix Anal. Appl. 13 (1992) 1015\u20131038.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR45","doi-asserted-by":"publisher","first-page":"138","DOI":"10.1137\/S0895479892241913","volume":"16","author":"H. Park","year":"1995","unstructured":"H. Park and L. Eld\u00e9n, Downdating the rank revealing URV decomposition, SIAM J. Matrix Anal. Appl. 16 (1995) 138\u2013155.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR46","first-page":"25","volume":"4","author":"H. Park","year":"1994","unstructured":"H. Park, S. Van Huffel and L. Eld\u00e9n, Fast algorithms for exponential data modeling, in: Proc. of 1994 IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing (ICASSP), April 19\u201322, Adela\u00efde, Australia, Vol. 4 (1994) pp. 25\u201328.","journal-title":"Proc. of 1994 IEEE Internat. Conf. on Acoustics, Speech, and Signal Processing (ICASSP)"},{"key":"329305_CR47","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1137\/S0895479893244353","volume":"18","author":"D.J. Pierce","year":"1997","unstructured":"D.J. Pierce and J.G. Lewis, Sparse multifrontal rank-revealing QR factorization, SIAM J. Matrix Anal. Appl. 18 (1997) 159\u2013180.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR48","doi-asserted-by":"publisher","first-page":"1442","DOI":"10.1109\/TASSP.1987.1165059","volume":"35","author":"M.A. Rahman","year":"1987","unstructured":"M.A. Rahman and K. Yu, Total least squares approach for frequency estimation using linear prediction, IEEE Trans. ASSP 35 (1987) 1442\u20131454.","journal-title":"IEEE Trans. ASSP"},{"key":"329305_CR49","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1016\/0165-1684(91)90058-Q","volume":"25","author":"L.L. Scharf","year":"1991","unstructured":"L.L. Scharf, The SVD and reduced rank signal processing, Signal Processing 25 (1991) 113\u2013133.","journal-title":"Signal Processing"},{"key":"329305_CR50","doi-asserted-by":"publisher","first-page":"403","DOI":"10.1137\/0905030","volume":"5","author":"G.W. Stewart","year":"1984","unstructured":"G.W. Stewart, Rank degeneracy, SIAM J. Sci. Statist. Comput. 5 (1984) 403\u2013413.","journal-title":"SIAM J. Sci. Statist. Comput."},{"key":"329305_CR51","doi-asserted-by":"publisher","first-page":"1535","DOI":"10.1109\/78.139256","volume":"40","author":"G.W. Stewart","year":"1992","unstructured":"G.W. Stewart, An updating algorithm for subspace tracking, IEEE Trans. Signal Processing 40 (1992) 1535\u20131541.","journal-title":"IEEE Trans. Signal Processing"},{"key":"329305_CR52","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1137\/0614034","volume":"14","author":"G.W. Stewart","year":"1993","unstructured":"G.W. Stewart, Updating a rank-revealing ULV decomposition, SIAM J. Matrix Anal. Appl. 14 (1993) 494\u2013499.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR53","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1007\/978-94-015-8196-7_16","volume-title":"Linear Algebra for Large Scale and Real-Time Applications","author":"G.W. Stewart","year":"1993","unstructured":"G.W. Stewart, Determining rank in the presence of error in: Linear Algebra for Large Scale and Real-Time Applications, eds. M.S. Moonen, G.H. Golub and B.L.R. DeMoor (Kluwer Academic, Dordrecht, 1993) pp. 275\u2013292."},{"key":"329305_CR54","unstructured":"G.W. Stewart, UTV decompositions, in: Numerical Analysis, eds. D.F. Griffith and G.A. Watson 1993, Pitman Research Notes in Mathematical Sciences (New York, 1994)."},{"key":"329305_CR55","unstructured":"G.W. Stewart, A gap-revealing matrix decomposition, Report TR-3771, Dept. of Computer Science, University of Maryland (1997), to appear in SIAM J. Sci. Comput."},{"key":"329305_CR56","doi-asserted-by":"crossref","DOI":"10.1137\/1.9781611971408","volume-title":"Matrix Algorithms. Vol. I: Basic Decompositions","author":"G.W. Stewart","year":"1998","unstructured":"G.W. Stewart, Matrix Algorithms. Vol. I: Basic Decompositions (SIAM, Philadelphia, PA, 1998)."},{"key":"329305_CR57","unstructured":"M. Stewart and P. Van Dooren, Updating a generalized URV decomposition, SIAM J. Matrix Anal. Appl., to appear."},{"key":"329305_CR58","doi-asserted-by":"publisher","first-page":"975","DOI":"10.1109\/PROC.1982.12428","volume":"70","author":"D.W. Tufts","year":"1982","unstructured":"D.W. Tufts and R. Kumaresan, Estimation of frequencies of multiple sinusoids: Making linear prediction perform like maximum likelihood, Proc. IEEE 70 (1982) 975\u2013989.","journal-title":"Proc. IEEE"},{"key":"329305_CR59","volume-title":"SVD and Signal Processing, II, Algorithms, Analysis and Applications","author":"R. Vaccaro","year":"1991","unstructured":"R. Vaccaro, SVD and Signal Processing, II, Algorithms, Analysis and Applications (Elsevier, Amsterdam, 1991)."},{"key":"329305_CR60","unstructured":"R.J. Vaccaro, D.W. Tufts and G.F. Boudreaux-Bartels, Advances in principal component signal processing, in: [17] pp. 115\u2013146."},{"key":"329305_CR61","unstructured":"A. van der Veen and E.F. Deprettere, SVD-based low-rank approximations of rational models, in: [59] pp. 431\u2013454."},{"key":"329305_CR62","doi-asserted-by":"publisher","first-page":"101","DOI":"10.1007\/BF02142742","volume":"4","author":"S. Van Huffel","year":"1993","unstructured":"S. Van Huffel and H. Zha, An efficient total least squares algorithm based on a rank revealing two-sided orthogonal decomposition, Numerical Algorithms 4 (1993) 101\u2013133.","journal-title":"Numerical Algorithms"},{"key":"329305_CR63","doi-asserted-by":"publisher","first-page":"974","DOI":"10.1137\/S0895479890183848","volume":"15","author":"G. Xu","year":"1994","unstructured":"G. Xu and T. Kailath, Fast estimation of principle eigenspace using Lanczos algorithm, SIAM J. Matrix Anal. Appl. 15 (1994) 974\u2013994.","journal-title":"SIAM J. Matrix Anal. Appl."},{"key":"329305_CR64","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1109\/82.318942","volume":"41","author":"G. Xu","year":"1994","unstructured":"G. Xu, H. Zha, G.H. Golub and T. Kailath, Fast and robust algorithms for updating signal subspaces, IEEE Trans. Circuits Systems 41 (1994) 537\u2013549.","journal-title":"IEEE Trans. Circuits Systems"},{"key":"329305_CR65","doi-asserted-by":"crossref","first-page":"781","DOI":"10.1007\/BF02510414","volume":"38","author":"P.A. Yoon","year":"1998","unstructured":"P.A. Yoon and J.L. Barlow, An efficient rank detection procedure for modifying the ULV decomposition, BIT 38 (1998) 781\u2013801.","journal-title":"BIT"}],"container-title":["Numerical Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019112103049.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1023\/A:1019112103049\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1023\/A:1019112103049.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,7,7]],"date-time":"2025-07-07T06:48:49Z","timestamp":1751870929000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1023\/A:1019112103049"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1999,8]]},"references-count":65,"journal-issue":{"issue":"2-3","published-print":{"date-parts":[[1999,8]]}},"alternative-id":["329305"],"URL":"https:\/\/doi.org\/10.1023\/a:1019112103049","relation":{},"ISSN":["1017-1398","1572-9265"],"issn-type":[{"value":"1017-1398","type":"print"},{"value":"1572-9265","type":"electronic"}],"subject":[],"published":{"date-parts":[[1999,8]]}}}