Globally convergent homotopy methods: a tutorial
TLDR
Homotopy algorithms for solving nonlinear systems of (algebraic) equations, which are convergent for almost all choices of starting point, are globally convergent with probability one and exhibit a large amount of coarse grain parallelism.About:
This article is published in Applied Mathematics and Computation.The article was published on 1989-05-01 and is currently open access. It has received 123 citations till now. The article focuses on the topics: n-connected & Homotopy analysis method.read more
Citations
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ReportDOI
Multi-Sensor CSEM Technology for Buried Target Classification
Mark E. Everett,Cam Nguyen +1 more
TL;DR: This final report describes the accomplishments made within the SERDP project UX-1312, which consisted of three tasks: sensor prototype development, software development, and integrated system test.
Book ChapterDOI
Homotopy Methods in Control System Design and Analysis
TL;DR: In this article, a computationally effective probability-one homotopy algorithm is presented for the optimal projection formulation of the reduced-order model problem, together with some numerical results.
Journal ArticleDOI
A homotopy inversion method for Rayleigh wave dispersion data
TL;DR: In this article , the homotopy method (HM) is proposed to transform the nonlinear Rayleigh-wave dispersion equation into a linear equation system, which has global optimized property and less computational burden.
Proceedings ArticleDOI
Interference Alignment in Reduced-Rank MIMO Networks with Application to Dynamic TDD
TL;DR: In this article , the authors investigated the feasibility of rank deficient MIMO interference alignment in DynTDD by establishing the simultaneously necessary and sufficient conditions, and compared the achievable DoF of centralized and distributed IA feasibility with those of various distributed designs.
Dissertation
Comparison of modified Riks/Wempner and homotopy methods
TL;DR: This paper presents a meta-modelling system that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of developing and testing a novel and scalable model for this type of architecture.
References
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Book
Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Classics in Applied Mathematics, 16)
TL;DR: In this paper, Schnabel proposed a modular system of algorithms for unconstrained minimization and nonlinear equations, based on Newton's method for solving one equation in one unknown convergence of sequences of real numbers.
Book
Numerical methods for unconstrained optimization and nonlinear equations
TL;DR: Newton's Method for Nonlinear Equations and Unconstrained Minimization and methods for solving nonlinear least-squares problems with Special Structure.
Journal ArticleDOI
An incremental approach to the solution of snapping and buckling problems
TL;DR: In this paper, an incremental approach to the solution of buckling and snapping problems is explored, where the authors use the length of the equilibrium path as a control parameter, together with the second order iteration method of Newton.