• MultRoot

  • Referenced in 87 articles [sw00604]
  • MultRoot - -a Matlab package for computing polynomial roots and multiplicities MultRoot is a collection ... Matlab modules for accurate computation of polynomial roots, especially roots with non-trivial multiplicities ... blackbox-type software, MultRoot requires the polynomial coefficients as the only input, and outputs ... without using multiprecision arithmetic, even if the polynomial coefficients are inexact. A comprehensive test suite...
  • Bertini

  • Referenced in 150 articles [sw06683]
  • Numerical Algebraic Geometry. Software for solving polynomial systems. Finds isolated solutions using total-degree start...
  • Gfan

  • Referenced in 88 articles [sw04698]
  • varieties. These are polyhedral fans associated to polynomial ideals. The maximal cones of a Gröbner ... Gröbner basis. The tropical variety of a polynomial ideal is a certain subcomplex...
  • Normaliz

  • Referenced in 86 articles [sw00630]
  • series and the Hilbert (or Ehrhart) (quasi) polynomial under a Z-grading (for example ... weighted) Ehrhart series and Lebesgue integrals of polynomials over rational polytopes via NmzIntegrate, a description...
  • na20

  • Referenced in 68 articles [sw11505]
  • Design, analysis, and implementation of a multiprecision polynomial rootfinder. We present the design, analysis ... digits of the roots of a polynomial with complex coefficients. The real and the imaginary ... designed to deal also with numerically hard polynomials like those arising from the symbolic preprocessing ... systems of polynomial equations, where the degree and the size of the coefficients are typically...
  • HOMPACK

  • Referenced in 115 articles [sw05324]
  • included for the special case of polynomial systems...
  • gfun

  • Referenced in 112 articles [sw00344]
  • functions defined by linear differential equations with polynomial coefficients, there is a procedure to compute...
  • Maxima

  • Referenced in 111 articles [sw00560]
  • ordinary differential equations, systems of linear equations, polynomials, and sets, lists, vectors, matrices, and tensors...
  • ORTHPOL

  • Referenced in 64 articles [sw00659]
  • package of routines for generating orthogonal polynomials and Gauss‐type quadrature rules. A collection ... numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object ... term recurrence relation satisfied by the orthogonal polynomials. Once these are known, additional data ... generated, such as zeros of orthogonal polynomials and Gauss-type quadrature rules, for which routines...
  • BiCGstab

  • Referenced in 103 articles [sw04022]
  • investigations of the BiCG part and the polynomial part. The second one is used...
  • Risa/Asir

  • Referenced in 93 articles [sw00806]
  • operations, to algebraic objects, e.g., numbers and polynomials, which are already converted into internal forms...
  • LattE

  • Referenced in 93 articles [sw04654]
  • ability to directly compute integrals of polynomial functions over polytopes and in particular...
  • Plural

  • Referenced in 62 articles [sw00719]
  • system (CAS) developed for efficient computations with polynomials. We describe Plural as an extension ... Singular to noncommutative polynomial rings (G-/GR-algebras): to which structures does it apply, the prerequisites...
  • RAGlib

  • Referenced in 53 articles [sw00774]
  • library for real solving polynomial systems of equations and inequalities. RAGlib is a Maple package ... study of real solutions of polynomial systems of equations and inequalities such as testing ... RAGlib Maple package allows to solve polynomial systems of equations/inequalities over the reals. Provided functionalities...
  • RATH

  • Referenced in 84 articles [sw00779]
  • package RATH which outputs entirely automatically tanh-polynomial travelling solitary wave solutions of a given...
  • Tyrolean

  • Referenced in 84 articles [sw07830]
  • lexicographic path order, loop detection, matrix interpretation, polynomial interpretation, predictive labeling, recursive SCC, root-labeling...
  • SparsePOP

  • Referenced in 50 articles [sw04331]
  • SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation ... approximating a global optimal solution of a polynomial optimization problem (POP) proposed by Waki ... relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy...
  • Aztec

  • Referenced in 78 articles [sw12817]
  • Jacobi, block Jacobi, Gauss-Seidel, least-squares polynomials, and overlapping domain decomposition using sparse...
  • na10

  • Referenced in 41 articles [sw11511]
  • Numerical computation of polynomial zeros by means of Aberth’s method. n algorithm for computing ... polynomial zeros, based on Aberth’s method, is presented. The starting approximations are chosen ... numberk i of zeros of the polynomial contained in each annulusA i. As starting approximations ... exact zeros of a “nearby” polynomial. This implies the backward stability of our algorithm...