- Referenced in 435 articles
- clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...
- Referenced in 637 articles
- perform simple and sophisticated operations on multivaraiate polynomials and on various data related to them ... ideal of zero-dimensional schemes, Poincare’ series and Hilbert functions, factorization of polynomials, toric ideals...
- Referenced in 49 articles
- 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 ... with the numberk i of zeros of the polynomial contained in each annulusA ... computed approximations are the exact zeros of a “nearby” polynomial. This implies the backward stability...
- Referenced in 79 articles
- generated, such as zeros of orthogonal polynomials and Gauss-type quadrature rules, for which routines...
- Referenced in 48 articles
- specialised data structure for Boolean polynomials based on zero-suppressed binary decision diagrams, which...
- Referenced in 77 articles
- facilities for symbolic computations with systems of polynomial equations. In particular, it allows to compute ... recombination) handles zero-divisors and parameters. This permits triangular decomposition of polynomial equations...
- Referenced in 15 articles
- Algorithm 419: zeros of a complex polynomial [C2] The subroutine CPOLY is a Fortran program ... find all the zeros of a complex polynomial by the three-stage complex algorithm described ... Traub . (An algorithm for real polynomials is given in .) The algorithm is similar ... zeros one at a time in roughly increasing order of modulus and deflates the polynomial...
- Referenced in 121 articles
- qualitatively different algorithms for tracking the homotopy zero curve: ordinary differential equation-based, normal flow ... included for the special case of polynomial systems...
- Referenced in 21 articles
- Newton polytopes of a general semi-mixed polynomial system through dynamic enumeration of all mixed ... role for computing all isolated zeros of a polynomial system by polyhedral homotopy continuation method...
- Referenced in 3 articles
- step procedure for simultaneous finding of polynomial zeros. The aim of this paper ... where each interval contains a zero of a polynomial. The IZSS1 method will produce successively ... that are guaranteed to still contain the zeros. The convergence rate of the procedure IZSS1 ... procedure is run on five test polynomials and the results obtained show that the modified...
- Referenced in 10 articles
- visualized are given by the zero set of a polynomial equation in 3 variables. Surfer...
- Referenced in 45 articles
- Jacobian matrix – are provided for tracking homotopy zero curves, as well as separate routines ... level driver for the special case of polynomial systems is also provided. Changes to HOMPACK...
- Referenced in 6 articles
- compute all the zeros of a quasi-polynomial located in a given region...
- Referenced in 3 articles
- computing characteristic sets and various zero decompositions of polynomial systems and other related polynomial calculations ... systems of polynomial equations, and factorizing multivariate polynomials over algebraic extension fields. A new module ... corresponding zero decompositions for systems of ordinary differential polynomials. Some of the routines from...
- Referenced in 76 articles
- polyhedral homotopy continuation method for solving polynomial systems. It updates its original version HOM4PS ... surpasses the existing packages in finding isolated zeros, such as PHCpack [J. Verschelde, ACM Trans...
- Referenced in 53 articles
- value is zero or is different from zero but small in Lanczos type algorithms ... avoided by considering only the existing orthogonal polynomials in the Lanczos type algorithms. The methods...
- Referenced in 31 articles
- left eigenvectors of dense quadratic matrix polynomials. It incorporates scaling of the problem parameters prior ... preprocessing step that reveals and deflates the zero and infinite eigenvalues contributed by singular leading...
- Referenced in 1 article
- based on the Gauss-Legendre polynomials zeros and allows one to create strict orthogonal expansion...
- Referenced in 9 articles
- case of polynomial rings with coefficients in a field of characteristic zero, the notion ... saturated strongly stable ideals in a given polynomial ring with a given Hilbert polynomial...