Polynomials and the exponent of matrix multiplication
L Chiantini, JD Hauenstein, C Ikenmeyer… - Bulletin of the …, 2018 - Wiley Online Library
The exponent of matrix multiplication is the smallest constant ω such that two n× n matrices
may be multiplied by performing O (n ω+ ε) arithmetic operations for every ε> 0. Determining …
may be multiplied by performing O (n ω+ ε) arithmetic operations for every ε> 0. Determining …
On deflation and multiplicity structure
This paper presents two new constructions related to singular solutions of polynomial
systems. The first is a new deflation method for an isolated singular root. This construction …
systems. The first is a new deflation method for an isolated singular root. This construction …
Verifyrealroots: a matlab package for computing verified real solutions of polynomials systems of equations and inequalities
VerifyRealRoots is a Matlab package for computing and verifying real solutions of
polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding …
polynomial systems of equations and inequalities. It calls Bertini or MMCRSolver for finding …
Certifying isolated singular points and their multiplicity structure
This paper presents two new constructions related to singular solutions of polynomial
systems. The first is a new deflation method for an isolated singular root. This con-struction …
systems. The first is a new deflation method for an isolated singular root. This con-struction …
Solution to the economic emission dispatch problem using numerical polynomial homotopy continuation
OI Barbosa-Ayala, JA Montañez-Barrera… - Energies, 2020 - mdpi.com
The economic emission dispatch (EED) is a highly constrained nonlinear multiobjective
optimization problem with a convex (or nonconvex) solution space. These characteristics …
optimization problem with a convex (or nonconvex) solution space. These characteristics …
Effective certification of approximate solutions to systems of equations involving analytic functions
We develop algorithms for certifying an approximation to a nonsingular solution of a square
system of equations built from univariate analytic functions. These algorithms are based on …
system of equations built from univariate analytic functions. These algorithms are based on …
A certified iterative method for isolated singular roots
In this paper we provide a new method to certify that a nearby polynomial system has a
singular isolated root and we compute its multiplicity structure. More precisely, given a …
singular isolated root and we compute its multiplicity structure. More precisely, given a …
On isolation of simple multiple zeros and clusters of zeros of polynomial systems
Given a well-constrained polynomial system $ f $ associated with a simple multiple zero $ x
$ of multiplicity $\mu $, we give a computable separation bound for isolating $ x $ from the …
$ of multiplicity $\mu $, we give a computable separation bound for isolating $ x $ from the …
Improved two-step Newton's method for computing simple multiple zeros of polynomial systems
Given a polynomial system f that is associated with an isolated singular zero ξ whose
Jacobian matrix is of corank one, and an approximate zero x that is close to ξ, we propose …
Jacobian matrix is of corank one, and an approximate zero x that is close to ξ, we propose …
Certification for polynomial systems via square subsystems
We consider numerical certification of approximate solutions to a system of polynomial
equations with more equations than unknowns by first certifying solutions to a square …
equations with more equations than unknowns by first certifying solutions to a square …