Piecewise-Linear Homotopy Algorithms for Sparse Systems of Nonlinear Equations

Michael J. Todd

doi:10.1137/0321011

Piecewise-Linear Homotopy Algorithms for Sparse Systems of Nonlinear Equations

SIAM Journal on Control and Optimization ◽

10.1137/0321011 ◽

1983 ◽

Vol 21 (2) ◽

pp. 204-214 ◽

Cited By ~ 5

Author(s):

Michael J. Todd

Keyword(s):

Nonlinear Equations ◽

Piecewise Linear ◽

Systems Of Nonlinear Equations ◽

Piecewise Linear Homotopy ◽

Sparse Systems ◽

Homotopy Algorithms

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A robust approach for finding all well-separated solutions of sparse systems of nonlinear equations

Numerical Algorithms ◽

10.1007/s11075-016-0249-x ◽

2016 ◽

Vol 76 (1) ◽

pp. 163-189 ◽

Cited By ~ 3

Author(s):

Ali Baharev ◽

Ferenc Domes ◽

Arnold Neumaier

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Robust Approach ◽

Sparse Systems

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Truncated Trust Region Methods Based on Preconditioned Iterative Subalgorithms for Large Sparse Systems of Nonlinear Equations

Journal of Optimization Theory and Applications ◽

10.1023/a:1022678023392 ◽

1997 ◽

Vol 95 (3) ◽

pp. 637-658 ◽

Cited By ~ 7

Author(s):

L. Lukšan ◽

J. Vlček

Keyword(s):

Nonlinear Equations ◽

Trust Region ◽

Systems Of Nonlinear Equations ◽

Trust Region Methods ◽

Sparse Systems ◽

Preconditioned Iterative ◽

Large Sparse Systems

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A globally convergent Newton-GMRES method for large sparse systems of nonlinear equations

Applied Numerical Mathematics ◽

10.1016/j.apnum.2006.02.007 ◽

2007 ◽

Vol 57 (3) ◽

pp. 235-252 ◽

Cited By ~ 48

Author(s):

Heng-Bin An ◽

Zhong-Zhi Bai

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Gmres Method ◽

Globally Convergent ◽

Sparse Systems ◽

Large Sparse Systems

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Inexact Quasi-Newton methods for sparse systems of nonlinear equations

Future Generation Computer Systems ◽

10.1016/s0167-739x(00)00074-1 ◽

2001 ◽

Vol 18 (1) ◽

pp. 41-53 ◽

Cited By ~ 11

Author(s):

Luca Bergamaschi ◽

Igor Moret ◽

Giovanni Zilli

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Newton Methods ◽

Sparse Systems ◽

Quasi Newton

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Tensor methods for large sparse systems of nonlinear equations

10.2172/434848 ◽

1996 ◽

Author(s):

A. Bouaricha ◽

R.B. Schnabel

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Tensor Methods ◽

Sparse Systems ◽

Large Sparse Systems

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Secant methods for sparse systems of nonlinear equations with a special structure

Computing ◽

10.1007/bf02253894 ◽

1983 ◽

Vol 30 (3) ◽

pp. 213-223 ◽

Cited By ~ 3

Author(s):

W. Mönch

Keyword(s):

Nonlinear Equations ◽

Special Structure ◽

Systems Of Nonlinear Equations ◽

Secant Methods ◽

Sparse Systems

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On the computational complexity of piecewise-linear homotopy algorithms

Mathematical Programming ◽

10.1007/bf01585104 ◽

1982 ◽

Vol 24 (1) ◽

pp. 216-224 ◽

Cited By ~ 11

Author(s):

Michael J. Todd

Keyword(s):

Computational Complexity ◽

Piecewise Linear ◽

Piecewise Linear Homotopy ◽

Homotopy Algorithms

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A note on solution of large sparse systems of nonlinear equations

Journal of Mathematical Analysis and Applications ◽

10.1016/0022-247x(78)90089-6 ◽

1978 ◽

Vol 63 (2) ◽

pp. 439-445 ◽

Cited By ~ 27

Author(s):

R.P Tewarson ◽

J.L Stephenson ◽

L.L Juang

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Sparse Systems ◽

Large Sparse Systems

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Tensor methods for large sparse systems of nonlinear equations

Mathematical Programming ◽

10.1007/bf01580076 ◽

1998 ◽

Vol 82 (3) ◽

pp. 377-400 ◽

Cited By ~ 16

Author(s):

Ali Bouaricha ◽

Robert B. Schnabel

Keyword(s):

Nonlinear Equations ◽

Systems Of Nonlinear Equations ◽

Tensor Methods ◽

Sparse Systems ◽

Large Sparse Systems

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Exploiting structure in piecewise-linear homotopy algorithms for solving equations

Mathematical Programming ◽

10.1007/bf01588321 ◽

1980 ◽

Vol 18 (1) ◽

pp. 233-247 ◽

Cited By ~ 16

Author(s):

Michael J. Todd

Keyword(s):

Piecewise Linear ◽

Piecewise Linear Homotopy ◽

Solving Equations ◽

Homotopy Algorithms

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