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Numerical Solutions by the Continuation Method

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E. WasserstromAuthors Info & Claims

SIAM Review, Volume 15, Issue 1

Pages 89 - 119

https://doi.org/10.1137/1015003

Published: 01 January 1973 Publication History

Abstract

The continuation method is developed with a special emphasis on its suitability for numerical solutions on fast computers. Four problems are treated in detail : finding roots of a polynomial, boundary value problems of nonlinear equations, identification of parameters and eigenvalue problems of linear ordinary differential operators. Numerical results are given for these problems. Finally, the continuation method is compared to iterative methods and several schemes which combine them are proposed.

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Lin XYang ZZhang XZhang QKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Continuation path learning for homotopy optimizationProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619285(21288-21311)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619285
Elías-Miranda AVallejo-Aldana DSánchez-Vega FLópez-Monroy ARosales-Pérez AMuñiz-Sanchez V(2023)Curriculum learning and evolutionary optimization into deep learning for text classificationNeural Computing and Applications10.1007/s00521-023-08632-835:28(21129-21164)Online publication date: 3-Aug-2023
https://dl.acm.org/doi/10.1007/s00521-023-08632-8
Boyd J(2016)Tracing Multiple Solution Branches for Nonlinear Ordinary Differential EquationsJournal of Scientific Computing10.1007/s10915-016-0229-269:3(1115-1143)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10915-016-0229-2
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Numerical Solutions by the Continuation Method
1. Mathematics of computing
  1. Mathematical analysis
2. Theory of computation
  1. Design and analysis of algorithms

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SIAM Review Volume 15, Issue 1

1973

279 pages

ISSN:0036-1445

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 January 1973

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Lin XYang ZZhang XZhang QKrause ABrunskill ECho KEngelhardt BSabato SScarlett J(2023)Continuation path learning for homotopy optimizationProceedings of the 40th International Conference on Machine Learning10.5555/3618408.3619285(21288-21311)Online publication date: 23-Jul-2023
https://dl.acm.org/doi/10.5555/3618408.3619285
Elías-Miranda AVallejo-Aldana DSánchez-Vega FLópez-Monroy ARosales-Pérez AMuñiz-Sanchez V(2023)Curriculum learning and evolutionary optimization into deep learning for text classificationNeural Computing and Applications10.1007/s00521-023-08632-835:28(21129-21164)Online publication date: 3-Aug-2023
https://dl.acm.org/doi/10.1007/s00521-023-08632-8
Boyd J(2016)Tracing Multiple Solution Branches for Nonlinear Ordinary Differential EquationsJournal of Scientific Computing10.1007/s10915-016-0229-269:3(1115-1143)Online publication date: 1-Dec-2016
https://dl.acm.org/doi/10.1007/s10915-016-0229-2
Soussen CIdier JJunbo Duan Brie D(2015)Homotopy Based Algorithms for $\ell _{\scriptscriptstyle 0}$-Regularized Least-SquaresIEEE Transactions on Signal Processing10.1109/TSP.2015.242147663:13(3301-3316)Online publication date: 1-Jul-2015
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Chenxi Hu Reeves S(2015)Trust Region Methods for the Estimation of a Complex Exponential Decay Model in MRI With a Single-Shot or Multi-Shot TrajectoryIEEE Transactions on Image Processing10.1109/TIP.2015.244291724:11(3694-3706)Online publication date: 1-Nov-2015
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Nikolova MNg MTam C(2010)Fast nonconvex nonsmooth minimization methods for image restoration and reconstructionIEEE Transactions on Image Processing10.1109/TIP.2010.205227519:12(3073-3088)Online publication date: 1-Dec-2010
https://dl.acm.org/doi/10.1109/TIP.2010.2052275
Jiang HDrew MLi Z(2007)Matching by Linear Programming and Successive ConvexificationIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2007.104829:6(959-975)Online publication date: 1-Jun-2007
https://dl.acm.org/doi/10.1109/TPAMI.2007.1048
Allgower EGeorg K(2006)Simplicial and Continuation Methods for Approximating Fixed Points and Solutions to Systems of EquationsSIAM Review10.1137/102200322:1(28-85)Online publication date: 10-Jul-2006
https://dl.acm.org/doi/10.1137/1022003
Li SWang HChan KPetrou M(1997)Minimization of MRF Energy with Relaxation LabelingJournal of Mathematical Imaging and Vision10.1023/A:10082535059537:2(149-161)Online publication date: 1-Mar-1997
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Everett M(1996)Homotopy, Polynomial Equations, Gross Boundary Data, and Small Helmholtz SystemsJournal of Computational Physics10.1006/jcph.1996.0070124:2(431-441)Online publication date: 15-Mar-1996
https://dl.acm.org/doi/10.1006/jcph.1996.0070
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Numerical solutions for fractional differential equations by Tau-Collocation method

Numerical solutions for systems of fractional differential equations by the decomposition method

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