Numerical mathematics: theory and computer applications
Numerical mathematics: theory and computer applications
A homotopy for solving general polynomial systems that respects m-homogenous structures
Applied Mathematics and Computation
On a theorem of S. Smale about Newton's method for analytic mappings
Applied Mathematics Letters
Numerical continuation methods: an introduction
Numerical continuation methods: an introduction
Numerical analysis: an introduction
Numerical analysis: an introduction
Algorithm 777: HOMPACK90: a suite of Fortran 90 codes for globally convergent homotopy algorithms
ACM Transactions on Mathematical Software (TOMS)
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
A Method for Computing All Solutions to Systems of Polynomials Equations
ACM Transactions on Mathematical Software (TOMS)
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Computing a zero of a smooth function is an old and extensively researched problem in numerical computation. While a large body of results and algorithms has been reported on this problem in the literature, to the extent we are aware, the published literature does not contain a globally convergent algorithm for finding a zero of an arbitrary smooth function. In this paper we present the first globally convergent algorithm for computing a zero (if one exists) of a general smooth function. After presenting the algorithm and a proof of global convergence, we also clarify the connection between our algorithm and some known results in topological degree theory.