The Conjugate Residual Method for Constrained Minimization Problems
1970; Society for Industrial and Applied Mathematics; Volume: 7; Issue: 3 Linguagem: Inglês
10.1137/0707032
ISSN1095-7170
Autores Tópico(s)Sparse and Compressive Sensing Techniques
ResumoPrevious article Next article The Conjugate Residual Method for Constrained Minimization ProblemsDavid G. LuenbergerDavid G. Luenbergerhttps://doi.org/10.1137/0707032PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Magnus R. Hestenes and , Eduard Stiefel, Methods of conjugate gradients for solving linear systems, J. Research Nat. Bur. Standards, 49 (1952), 409–436 (1953) MR0060307 0048.09901 CrossrefISIGoogle Scholar[2] Magnus R. Hestenes, The conjugate-gradient method for solving linear systems, Proceedings of Symposia in Applied Mathematics. Vol. VI. Numerical analysis, McGraw-Hill Book Company, Inc., New York, for the American Mathematical Society, Providence, R. I., 1956, 83–102 MR0084178 0072.14102 Google Scholar[3] F. S. Beckman, A. Ralston and , H. S. Wilf, The solution of linear equations by the conjugate gradient methodMathematical methods for digital computers, Wiley, New York, 1960, 62–72 MR0117910 Google Scholar[4] Henry A. Antosiewicz and , Werner C. Rheinboldt, J. Todd, Numerical analysis and functional analysisSurvey of numerical analysis, McGraw-Hill, New York, 1962, 485–517, Chap. 14. MR0138185 Google Scholar[5] David G. Luenberger, Optimization by vector space methods, John Wiley & Sons Inc., New York, 1969xvii+326 MR0238472 0176.12701 Google Scholar[6] David G. Luenberger, Hyperbolic pairs in the method of conjugate gradients, SIAM J. Appl. Math., 17 (1969), 1263–1267 10.1137/0117118 MR0260153 0187.09704 LinkISIGoogle Scholar[7] B. V. Shah, , R. J. Buehler and , O. Kempthorne, Some algorithms for minimizing a function of several variables, J. Soc. Indust. Appl. Math., 12 (1964), 74–92 10.1137/0112007 MR0165655 0127.33902 LinkISIGoogle Scholar[8] Phillip Wolfe, J. Abadie, Methods of nonlinear programmingNonlinear Programming (NATO Summer School, Menton, 1964), North-Holland, Amsterdam, 1967, 97–131 MR0216868 0178.22802 Google Scholar[9] James W. Daniel, The conjugate gradient method for linear and nonlinear operator equations, SIAM J. Numer. Anal., 4 (1967), 10–26 10.1137/0704002 MR0217987 0154.40302 LinkGoogle Scholar[10] James W. Daniel, Convergence of the conjugate gradient method with computationally convenient modifications, Numer. Math., 10 (1967), 125–131 10.1007/BF02174144 MR0219232 0178.18302 CrossrefISIGoogle Scholar[11] R. Fletcher and , C. M. Reeves, Function minimization by conjugate gradients, Comput. J., 7 (1964), 149–154 10.1093/comjnl/7.2.149 MR0187375 0132.11701 CrossrefISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Iterative Solvers for Mixed Problems6 July 2022 Cross Ref Primal–Dual Methods20 August 2021 Cross Ref Conjugate Direction Methods20 August 2021 Cross Ref Efficient and Accurate Collision Response for Elastically Deformable ModelsACM Transactions on Graphics, Vol. 38, No. 2 Cross Ref The Conjugate Residual Method in Linesearch and Trust-Region MethodsMarie-Ange Dahito and Dominique Orban25 July 2019 | SIAM Journal on Optimization, Vol. 29, No. 3AbstractPDF (977 KB)Correction of low-Reynolds number turbulence model to hydrocarbon fuel at supercritical pressureAerospace Science and Technology, Vol. 77 Cross Ref Branch Cuts of Stokes Wave on Deep Water. Part I: Numerical Solution and Padé Approximation9 May 2016 | Studies in Applied Mathematics, Vol. 137, No. 4 Cross Ref Pipelined, Flexible Krylov Subspace MethodsP. Sanan, S.M. 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