Open AccessBook
Introduction to Numerical Continuation Methods
Eugene L. Allgower,Kurt Georg +1 more
- 01 Jan 1987
TL;DR: The Numerical Continuation Methods for Nonlinear Systems of Equations (NCME) as discussed by the authors is an excellent introduction to numerical continuuation methods for solving nonlinear systems of equations.
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Abstract: From the Publisher:
Introduction to Numerical Continuation Methods continues to be useful for researchers and graduate students in mathematics, sciences, engineering, economics, and business looking for an introduction to computational methods for solving a large variety of nonlinear systems of equations. A background in elementary analysis and linear algebra is adequate preparation for reading this book; some knowledge from a first course in numerical analysis may also be helpful.
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Citations
•Book
Computer Vision: Algorithms and Applications
Richard Szeliski
- 30 Sep 2010
TL;DR: Computer Vision: Algorithms and Applications explores the variety of techniques commonly used to analyze and interpret images and takes a scientific approach to basic vision problems, formulating physical models of the imaging process before inverting them to produce descriptions of a scene.
•Posted Content
Entropy-SGD: Biasing Gradient Descent Into Wide Valleys
Pratik Chaudhari,Pratik Chaudhari,Anna Choromanska,Stefano Soatto,Yann LeCun,Yann LeCun,Carlo Baldassi,Carlo Baldassi,Christian Borgs,Jennifer Chayes,Levent Sagun,Riccardo Zecchina,Riccardo Zecchina +12 more
TL;DR: This paper proposes a new optimization algorithm called Entropy-SGD for training deep neural networks that is motivated by the local geometry of the energy landscape and compares favorably to state-of-the-art techniques in terms of generalization error and training time.
617
Nonlinear normal modes, Part II: Toward a practical computation using numerical continuation techniques
TL;DR: In this paper, a nonlinear normal mode (NNM) computation is shown to be possible with limited implementation effort, which paves the way to a practical method for determining the NNMs of nonlinear mechanical systems.
550
References
•Book
Solutions of ill-posed problems
Andreĭ Nikolaevich Tikhonov,Vasiliy Yakovlevich Arsenin +1 more
- 01 Jan 1977
9.9K
Methods of Conjugate Gradients for Solving Linear Systems
TL;DR: An iterative algorithm is given for solving a system Ax=k of n linear equations in n unknowns and it is shown that this method is a special case of a very general method which also includes Gaussian elimination.
•Book
Numerical methods for unconstrained optimization and nonlinear equations
John E. Dennis,Robert B. Schnabel +1 more
- 01 Mar 1983
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
8.2K
•Book
Iterative Solution of Nonlinear Equations in Several Variables
J.M. Ortega,Werner C. Rheinboldt +1 more
- 01 Jun 1970
TL;DR: In this article, the authors present a list of basic reference books for convergence of Minimization Methods in linear algebra and linear algebra with a focus on convergence under partial ordering.
7.9K
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