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Polynomial Homotopy Continuation with PHCpack
, 2010
"... PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems with as ma ..."
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Cited by 10 (2 self)
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PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems
Polynomial Homotopy Continuation with PHCpack∗
"... PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems with as m ..."
Abstract
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PHCpack is a software package to solve polynomial systems via homotopy continuation methods. In the last twenty years (since the start of the development of PHCpack), the notion of solving a polynomial system by PHCpack evolved from approximating all isolated complex solutions for systems
Homotopy Continuation For Sparse Signal Representation
 In Prceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing
, 2005
"... We explore the application of a homotopy continuationbased method for sparse signal representation in overcomplete dictionaries. Our problem setup is based on the basis pursuit framework, which involves a convex optimization problem consisting of terms enforcing data fidelity and sparsity, balanced ..."
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We explore the application of a homotopy continuationbased method for sparse signal representation in overcomplete dictionaries. Our problem setup is based on the basis pursuit framework, which involves a convex optimization problem consisting of terms enforcing data fidelity and sparsity
Homotopy Continuation Methods For Solving Polynomial Systems
, 1996
"... Homotopy continuation methods have been proven to be reliable for computing numerically approximations to all isolated solutions of polynomial systems. The performance of... ..."
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Cited by 19 (1 self)
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Homotopy continuation methods have been proven to be reliable for computing numerically approximations to all isolated solutions of polynomial systems. The performance of...
Computing Monodromy via Parallel Homotopy Continuation
"... Numerical homotopy continuation gives a powerful tool for the applied scientist who seeks solutions to a system of polynomial equations. Techniques from numerical homotopy continuation can also be useful in pure mathematical research. We discuss applications of a particular homotopy continuation ide ..."
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Numerical homotopy continuation gives a powerful tool for the applied scientist who seeks solutions to a system of polynomial equations. Techniques from numerical homotopy continuation can also be useful in pure mathematical research. We discuss applications of a particular homotopy continuation
HOMOTOPY CONTINUATION METHODS FOR NONLINEAR COMPLEMENTARITY PROBLEMS
, 1991
"... A complementarity problem with a continuous mapping f from Rn into itself can be written as the system of equations F(x, y) = 0 and (x, y)> 0. Here F is the mapping from R ~ " into itself defined by F(x, y) = ( xl y,, x2yZ,..., x, ~ ye, y ffx)). Under the assumption that the mapping f is ..."
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Cited by 44 (3 self)
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is a P,,function, we study various aspects of homotopy continuation methods that trace a trajectory consisting of solutions of the family of systems of equations F(x, y) = t(a, b) and (x, y) 8 0 until the parameter t> 0 attains 0. Here (a, b) denotes a 2ndimensional constant positive vector. We
SymbolicNumeric Completion of Differential Systems by Homotopy Continuation
 Proc. ISSAC 2005. ACM
, 2005
"... Two ideas are combined to construct a hybrid symbolicnumeric differentialelimination method for identifying and including missing constraints arising in differential systems. First we exploit the fact that a system once differentiated becomes linear in its highest derivatives. Then we apply diagona ..."
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Cited by 5 (2 self)
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diagonal homotopies to incrementally process new constraints, one at a time. The method is illustrated on several examples, combining symbolic differential elimination (using rifsimp) with numerical homotopy continuation (using phc).
A homotopy continuation solution of the covariance extension equation
 in New Directions and Applications in Control Theory
, 2005
"... Algebraic geometry plays an important role in the theory of linear systems for (at least) three reasons. First, the Laplace transform turns expressions about linear differential systems into expressions involving rational functions. In addition, many of the transformations studied in linear systems ..."
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Cited by 3 (3 self)
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of the standard Riccati equation. Nonetheless, we prove the existence and uniqueness of a positive semidefinite solution. We also show that this equation has the proper geometric attributes to be solvable by homotopy continuation methods, which we illustrate in several examples. 1 The covariance extension
Numerical Stability of Path Tracing in Polyhedral Homotopy Continuation Methods
, 2003
"... The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and illconditioned Jacobian matrices encountered in tracing of homotop ..."
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Cited by 6 (1 self)
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The reliability of polyhedral homotopy continuation methods for solving a polynomial system becomes increasingly important as the dimension of the polynomial system increases. High powers of the homotopy continuation parameter t and illconditioned Jacobian matrices encountered in tracing
Numerical Polynomial Homotopy Continuation Method and String Vacua
 Adv.High Energy Phys
, 2011
"... iv ..."
Results 1  10
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31,752