Rounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process

Giraud, L. - Langou, J. - Rozložník, Miroslav - van den Eshof, J.
Rounding Error Analysis of the Classical Gram-Schmidt Orthogonalization Process.
Numerische Mathematik. Roč. 101, - (2005), s. 87-100. ISSN 0029-599X. E-ISSN 0945-3245
Impact factor: 1.222, year: 2005
http://hdl.handle.net/11104/0125442

Cited: 40

--- ANDRLE, M. - REBOLLO-NEIRA, L. Experiments on orthogonalization by biorthogonal representations of orthogonal projectors. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, AUG 1 2007, vol. 205, no. 1, p. 545-551. [WOS]
--- COURRIEU, P. Fast solving of weighted pairing least-squares systems. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, SEP 1 2009, vol. 231, no. 1, p. 39-48. [WOS]
--- SOMMARIVA, A. - VIANELLO, M. Computing approximate Fekete points by QR factorizations of Vandermonde matrices. COMPUTERS & MATHEMATICS WITH APPLICATIONS. ISSN 0898-1221, APR 2009, vol. 57, no. 8, p. 1324-1336. [WOS]
--- TRIFONOV, P. - COSTA, E. Adaptive data transmission in downlink MIMO-OFDM systems with pre-equalization. 2007 IEEE INTERNATIONAL CONFERENCE ON COMMUNICATIONS, VOLS 1-14. ISSN 1550-3607, 2007, p. 1036-1041. [WOS]
--- ROLLIN, S. - FICHTNER, W. Improving the accuracy of GMRES with deflated restarting. SIAM JOURNAL ON SCIENTIFIC COMPUTING. ISSN 1064-8275, 2007, vol. 30, no. 1, p. 232-245. [WOS]
--- NGOC, D.T.B. - OGAWA, M. Overflow and Roundoff Error Analysis via Model Checking. SEFM 2009: SEVENTH INTERNATIONAL CONFERENCE ON SOFTWARE ENGINEERING AND FORMAL METHODS. 2009, p. 105-114. [WOS]
--- GENTILE, M. - SOMMARIVA, A. - VIANELLO, M. Polynomial interpolation and cubature over polygons. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, JUL 1 2011, vol. 235, no. 17, p. 5232-5239. [WOS]
--- STEWART, G.W. ON THE NUMERICAL ANALYSIS OF OBLIQUE PROJECTORS. SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS. ISSN 0895-4798, 2011, vol. 32, no. 1, p. 309-348. [WOS]
--- DUBOIS, J. - CALVIN, C. - PETITON, S. Performance and Numerical Accuracy Evaluation of Heterogeneous Multicore Systems for Krylov Orthogonal Basis Computation. HIGH PERFORMANCE COMPUTING FOR COMPUTATIONAL SCIENCE - VECPAR 2010. ISSN 0302-9743, 2011, vol. 6449, p. 45-57. [WOS]
--- BOS, L. - SOMMARIVA, A. - VIANELLO, M. Least-squares polynomial approximation on weakly admissible meshes: Disk and triangle. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS. ISSN 0377-0427, DEC 1 2010, vol. 235, no. 3, p. 660-668. [WOS]
--- BOS, L. - DE MARCHI, S. - SOMMARIVA, A. - VIANELLO, M. COMPUTING MULTIVARIATE FEKETE AND LEJA POINTS BY NUMERICAL LINEAR ALGEBRA. SIAM JOURNAL ON NUMERICAL ANALYSIS. ISSN 0036-1429, 2010, vol. 48, no. 5, p. 1984-1999. [WOS]
--- KAVAN, L. - SLOAN, P.P. - O'SULLIVAN, C. Fast and Efficient Skinning of Animated Meshes. COMPUTER GRAPHICS FORUM. ISSN 0167-7055, 2010, vol. 29, no. 2, p. 327-336. [WOS]
--- KIANI, M. Extensions to the modified Gram-Schmidt strategy and its application in the steepest ascent method. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION. ISSN 0094-9655, 2010, vol. 80, no. 4, p. 389-400. [WOS]
--- FIELD, S.E. - GALLEY, C.R. - HESTHAVEN, J.S. - KAYE, J. - TIGLIO, M. Fast Prediction and Evaluation of Gravitational Waveforms Using Surrogate Models. PHYSICAL REVIEW X. ISSN 2160-3308, JUL 14 2014, vol. 4, no. 3. [WOS]
--- BARLOW, J.L. BLOCK GRAM-SCHMIDT DOWNDATING. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2014, vol. 43, p. 163-187. [WOS]
--- CHEN, P. - QUARTERONI, A. Accurate and efficient evaluation of failure probability for partial different equations with random input data. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING. ISSN 0045-7825, DEC 1 2013, vol. 267, p. 233-260. [WOS]
--- LEON, S.J. - BJORCK, A. - GANDER, W. Gram-Schmidt orthogonalization: 100 years and more. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. ISSN 1070-5325, MAY 2013, vol. 20, no. 3, p. 492-532. [WOS]
--- BARLOW, J.L. - SMOKTUNOWICZ, A. Reorthogonalized block classical Gram-Schmidt. NUMERISCHE MATHEMATIK. ISSN 0029-599X, MAR 2013, vol. 123, no. 3, p. 395-423. [WOS]
--- ARNST, M. - GHANEM, R. - PHIPPS, E. - RED-HORSE, J. Measure transformation and efficient quadrature in reduced-dimensional stochastic modeling of coupled problems. INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING. ISSN 0029-5981, DEC 21 2012, vol. 92, no. 12, p. 1044-1080. [WOS]
--- ALIAGA, J.I. - BIENTINESI, P. - DAVIDOVIC, D. - DI NAPOLI, E. - IGUAL, F.D. - QUINTANA-ORTI, E.S. Solving dense generalized eigenproblems on multi-threaded architectures. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, JUL 15 2012, vol. 218, no. 22, p. 11279-11289. [WOS]
--- SMOKTUNOWICZ, A. - WROBEL, I. Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices. BIT NUMERICAL MATHEMATICS. ISSN 0006-3835, JUN 2012, vol. 52, no. 2, p. 503-524. [WOS]
--- SAJID, I.A. - AHMED, M.M. - SAGHEER, M. AN OPTIMIZED FACE RECOGNITION SYSTEM USING STABLE ORTHOGONALIZATION. INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL. ISSN 1349-4198, JAN 2012, vol. 8, no. 1A, p. 219-232. [WOS]
--- GENTILE, M. - SOMMARIVA, A. - VIANELLO, M. Polynomial approximation and quadrature on geographic rectangles. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, MAR 15 2017, vol. 297, p. 159-179. [WOS]
--- KIANI, M. The augmentation of existing data for improving the path of steepest ascent. COMMUNICATIONS IN STATISTICS-THEORY AND METHODS. ISSN 0361-0926, 2017, vol. 46, no. 5, p. 2506-2518. [WOS]
--- KRAMER, B. - SINGLER, J.R. A POD PROJECTION METHOD FOR LARGE-SCALE ALGEBRAIC RICCATI EQUATIONS. NUMERICAL ALGEBRA CONTROL AND OPTIMIZATION. ISSN 2155-3289, DEC 2016, vol. 6, no. 4, p. 413-435. [WOS]
--- LI, R.P. - XI, Y.Z. - SAAD, Y. Schur complement-based domain decomposition preconditioners with low-rank corrections. NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS. ISSN 1070-5325, AUG 2016, vol. 23, no. 4, p. 706-729. [WOS]
--- LI, R.P. - XI, Y.Z. - VECHARYNSKI, E. - YANG, C. - SAAD, Y. A THICK-RESTART LANCZOS ALGORITHM WITH POLYNOMIAL FILTERING FOR HERMITIAN EIGENVALUE PROBLEMS. SIAM JOURNAL ON SCIENTIFIC COMPUTING. ISSN 1064-8275, 2016, vol. 38, no. 4, p. A2512-A2534. [WOS]
--- SORENSEN, D.C. - EMBREE, M. A DEIM INDUCED CUR FACTORIZATION. SIAM JOURNAL ON SCIENTIFIC COMPUTING. ISSN 1064-8275, 2016, vol. 38, no. 3, p. A1454-A1482. [WOS]
--- SOMMARIVA, A. - VIANELLO, M. COMPRESSION OF MULTIVARIATE DISCRETE MEASURES AND APPLICATIONS. NUMERICAL FUNCTIONAL ANALYSIS AND OPTIMIZATION. ISSN 0163-0563, SEP 2 2015, vol. 36, no. 9, p. 1198-1223. [WOS]
--- LIU, W.J. - XIE, W.C. - TONG, H.B. - WANG, H.L. - ZHOU, C. - WANG, Y.L. Adaptive coherence estimator based on the Krylov subspace technique for airborne radar. JOURNAL OF SYSTEMS ENGINEERING AND ELECTRONICS. ISSN 1004-4132, AUG 2015, vol. 26, no. 4, p. 705-712. [WOS]
--- SOMMARIVA, A. - VIANELLO, M. Polynomial fitting and interpolation on circular sections. APPLIED MATHEMATICS AND COMPUTATION. ISSN 0096-3003, MAY 1 2015, vol. 258, p. 410-424. [WOS]
--- HEGEDUS, C.J. Reorthogonalization Methods Revisited. ACTA POLYTECHNICA HUNGARICA. ISSN 1785-8860, 2015, vol. 12, no. 8, p. 7-26. [WOS]
--- YAMAMOTO, Y. - NAKATSUKASA, Y. - YANAGISAWA, Y. - FUKAYA, T. ROUNDOFF ERROR ANALYSIS OF THE CHOLESKYQR2 ALGORITHM. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2015, vol. 44, p. 306-326. [WOS]
--- ZHENG, Y. - CAO, Y. - CHANG, C.H. UDhashing: Physical Unclonable Function-Based User-Device Hash for Endpoint Authentication. IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS. ISSN 0278-0046, DEC 2019, vol. 66, no. 12, p. 9559-9570. [WOS]
--- ANANTHARAMU, S. - MAHESH, K. A parallel and streaming Dynamic Mode Decomposition algorithm with finite precision error analysis for large data. JOURNAL OF COMPUTATIONAL PHYSICS. ISSN 0021-9991, MAR 1 2019, vol. 380, p. 355-377. [WOS]
--- CHANG, Y.C. - SHIAU, S.Y. - COMBESCOT, M. Crossover from trion-hole complex to exciton-polaron in n-doped two-dimensional semiconductor quantum wells. PHYSICAL REVIEW B. ISSN 2469-9950, DEC 14 2018, vol. 98, no. 23. [WOS]
--- RIVAZ, A. - MOGHADAM, M.M. - SADEGHI, D. - KERMANI, H.M. An approach of orthogonalization within the Gram-Schmidt algorithm. COMPUTATIONAL & APPLIED MATHEMATICS. ISSN 0101-8205, MAY 2018, vol. 37, no. 2, p. 1250-1262. [WOS]
--- SOMMARIVA, A. - VIANELLO, M. Numerical hyperinterpolation over nonstandard planar regions. MATHEMATICS AND COMPUTERS IN SIMULATION. ISSN 0378-4754, NOV 2017, vol. 141, SI, p. 110-120. [WOS]
--- IMBERTI, D. - ERHEL, J. VARYING THE S IN YOUR S-STEP GMRES. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2017, vol. 47, SI, p. 206-230. [WOS]
--- ZEMKE, J.P.M. VARIANTS OF IDR WITH PARTIAL ORTHONORMALIZATION. ELECTRONIC TRANSACTIONS ON NUMERICAL ANALYSIS. ISSN 1068-9613, 2017, vol. 46, p. 245-272. [WOS]