Abstract. We describe, for the first time, a completely rigorous homotopy (path–following) algo-rithm (in the Turing machine model) to find approximate zeros of systems of polynomial equations. If the coordinates of the input systems and the initial zero are rational our algorithm involves only rational computations and if the homotopy is well posed an approximate zero with integer coordi-nates of the target system is obtained. The total bit complexity is linear in the length of the path in the condition metric, and polynomial in the logarithm of the maximum of the condition number along the path, and in the size of the input. 1
Homotopies for polynomial systems provide computational evidence for a challenging instance of a con...
AbstractWe substantially improve the known algorithms for approximating all the complex zeros of an ...
AbstractSecant type methods are useful for finding zeros of analytic equations that include polynomi...
Abstract. We describe, for the first time, a completely rigorous homotopy (path–following) algo-rith...
Abstract. Given a homotopy connecting two polynomial sys-tems we provide a rigorous algorithm for tr...
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel...
The goal of this study is to extend the applicability of a homotopy method for locating an approxima...
In this paper, we present several algorithms for certified homotopy continuation. One typical applic...
Homotopy algorithms combine beautiful mathematics with the capability to solve complicated nonlinear...
The classical Theorem of Bézout yields an upper bound for the number of finite solutions to a given ...
Certain classes of nonlinear systems of equations, such as polynomial systems, have properties that ...
AbstractBy modifying and combining algorithms in symbolic and numerical computation, we propose a re...
AbstractWe define counting classes #PR and #PC in the Blum–Shub–Smale setting of computations over ...
An algorithm is given to compute the real points of the irreducible one-dimensional complex componen...
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently g...
Homotopies for polynomial systems provide computational evidence for a challenging instance of a con...
AbstractWe substantially improve the known algorithms for approximating all the complex zeros of an ...
AbstractSecant type methods are useful for finding zeros of analytic equations that include polynomi...
Abstract. We describe, for the first time, a completely rigorous homotopy (path–following) algo-rith...
Abstract. Given a homotopy connecting two polynomial sys-tems we provide a rigorous algorithm for tr...
We consider the problem of tracking one solution path defined by a polynomial homotopy on a parallel...
The goal of this study is to extend the applicability of a homotopy method for locating an approxima...
In this paper, we present several algorithms for certified homotopy continuation. One typical applic...
Homotopy algorithms combine beautiful mathematics with the capability to solve complicated nonlinear...
The classical Theorem of Bézout yields an upper bound for the number of finite solutions to a given ...
Certain classes of nonlinear systems of equations, such as polynomial systems, have properties that ...
AbstractBy modifying and combining algorithms in symbolic and numerical computation, we propose a re...
AbstractWe define counting classes #PR and #PC in the Blum–Shub–Smale setting of computations over ...
An algorithm is given to compute the real points of the irreducible one-dimensional complex componen...
A solution for Smale's 17th problem, for the case of systems with bounded degree was recently g...
Homotopies for polynomial systems provide computational evidence for a challenging instance of a con...
AbstractWe substantially improve the known algorithms for approximating all the complex zeros of an ...
AbstractSecant type methods are useful for finding zeros of analytic equations that include polynomi...