Complexity of Bezout's theorem V: polynomial time
Selected papers of the workshop on Continuous algorithms and complexity
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
An algorithm for the reduction of linear DAE
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Symbolic computation of the index of quasilinear differential-algebraic equations
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Existence and uniqueness theorems for formal power series solutions of analytic differential systems
ISSAC '99 Proceedings of the 1999 international symposium on Symbolic and algebraic computation
Algorithm 795: PHCpack: a general-purpose solver for polynomial systems by homotopy continuation
ACM Transactions on Mathematical Software (TOMS)
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
Deformation techniques for efficient polynomial equation solving
Journal of Complexity
Numerical homotopies to compute generic points on positive dimensional algebraic sets
Journal of Complexity
A probabilistic algorithm to test local algebraic observability in polynomial time
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations
Automatic differentiation of algorithms: from simulation to optimization
Automatic differentiation of algorithms: from simulation to optimization
Numerical Decomposition of the Solution Sets of Polynomial Systems into Irreducible Components
SIAM Journal on Numerical Analysis
Symmetric Functions Applied to Decomposing Solution Sets of Polynomial Systems
SIAM Journal on Numerical Analysis
A geometric-numeric algorithm for absolute factorization of multivariate polynomials
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra, 3/e (Undergraduate Texts in Mathematics)
A complete symbolic-numeric linear method for camera pose determination
ISSAC '03 Proceedings of the 2003 international symposium on Symbolic and algebraic computation
Fast computation of discrete invariants associated to a differential rational mapping
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Symbolic-numeric completion of differential systems by homotopy continuation
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Application of numerical algebraic geometry and numerical linear algebra to PDE
Proceedings of the 2006 international symposium on Symbolic and algebraic computation
Symbolic-numeric computation of implicit riquier bases for PDE
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Solving polynomial systems via symbolic-numeric reduction to geometric involutive form
Journal of Symbolic Computation
Hybrid method for solving new pose estimation equation system
IWMM'04/GIAE'04 Proceedings of the 6th international conference on Computer Algebra and Geometric Algebra with Applications
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Symbolic algorithms using a finite number of exact differentiations and eliminations are able to reduce over and under-determined systems of polynomially nonlinear differential equations to involutive form. The output involutive form enables the identification of consistent initial values, and eases the application of exact or numerical integration methods.Motivated to avoid expression swell of pure symbolic approaches and with the desire to handle systems with approximate coefficients, we propose the use of homotopy continuation methods to perform the differential-elimination process on such non-square systems. Examples such as the classic index 3 Pendulum illustrate the new procedure. Our approach uses slicing by random linear subspaces to intersect its jet components in finitely many points. Generation of enough generic points enables irreducible jet components of the differential system to be interpolated.