
INTLAB
 Referenced in 457 articles
[sw04004]
 systems (also inner inclusions and structured matrices) sparse s.p.d. linear systems systems of nonlinear equations ... clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real ... fast) interval arithmetic for real and complex sparse matrices (very fast) automatic differentiation (forward mode ... simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very...

SparsePOP
 Referenced in 66 articles
[sw04331]
 SparsePOP: a sparse semidefinite programming relaxation of polynomial optimization problems. SparsePOP is a Matlab implementation ... sparse semidefinite programming (SDP) relaxation method for approximating a global optimal solution of a polynomial ... sparse SDP relaxation exploits a sparse structure of polynomials in POPs when applying “a hierarchy...

Aztec
 Referenced in 83 articles
[sw12817]
 algorithms for the iterative solution of large sparse linear systems arising in scientific and engineering ... GaussSeidel, leastsquares polynomials, and overlapping domain decomposition using sparse LU, ILU, ILUT, BILU...

HOMPACK
 Referenced in 121 articles
[sw05324]
 sparse Jacobian matrices. A highlevel driver is included for the special case of polynomial...

HOMPACK90
 Referenced in 46 articles
[sw00412]
 sparse Jacobian matrices. A high level driver for the special case of polynomial systems ... modules, new end games, support for several sparse matrix data structures, and new iterative algorithms...

SYNAPS
 Referenced in 24 articles
[sw00941]
 vectors, matrices (dense, sparse, structured), univariate and multivariate polynomial (in the monomial, Horner or Bernstein...

SparseBSOS
 Referenced in 12 articles
[sw31772]
 large scale polynomial optimization with sparsity. We provide a sparse version of the bounded degree ... Comp Optim:87–117, 2017) for polynomial optimization problems. It permits to treat large scale ... pattern satisfies the running intersection property this SparseBSOS hierarchy of semidefinite programs (with semidefinite...

FOXBOX
 Referenced in 16 articles
[sw00307]
 compute the greatest common divisor and factorize polynomials in black box representation, producing as output ... compute the standard sparse distributed representation of a black box polynomial, for example, one which...

Lacunaryx
 Referenced in 4 articles
[sw20573]
 These algorithms take as input a polynomial in sparse representation, that is as a list ... complexity of these algorithms is polynomial in the sparse size of the input polynomial...

Audi
 Referenced in 3 articles
[sw19687]
 AuDi is internally powered by the truncated polynomial multiplication algorithm of the open source project ... described in: Biscani, Francesco. Parallel sparse polynomial multiplication on modern hardware architectures. Proceedings ... Biscani, Francesco. Multiplication of sparse Laurent polynomials and Poisson series on modern hardware architectures. arXiv...

ILUM
 Referenced in 63 articles
[sw07244]
 multielimination ILU preconditioner for general sparse matrices Standard preconditioning techniques based on incomplete ... consist of either using some form of polynomial precoditioning or applying the usual ILU factorization ... methods that deal specifically with general unstructured sparse matrices such as those arising from finite...

POLY
 Referenced in 5 articles
[sw11266]
 data structure for sparse distributed polynomials in the Maple kernel significantly accelerates a large subset...

Givaro
 Referenced in 7 articles
[sw00354]
 fields, Extensions Fields, Finite Fields, Finite Rings, Polynomials, Algebraic numbers, Arbitrary precision integers and rationals ... such as vectors, matrices (dense, sparse, structured), univariate polynomials (and therefore recursive multivariate). It contains...

Tensorlab
 Referenced in 63 articles
[sw14255]
 with structured factors and support for dense, sparse and incomplete data sets, tensor decompositions: canonical ... numerical complex differentiation, global minimization of bivariate polynomials and rational functions: both real and complex...

StdPoolingPolyAlgos
 Referenced in 5 articles
[sw34823]
 StdPoolingPolyAlgos: Implementation of polynomialtime algorithms for subclasses of single quality standard pooling problems ... structure in the pooling problem: from sparse stronglypolynomial solutions to NPhardness. The standard ... pooling problem sparsity and show that the sparse patterns of active topological structure are associated...

LCM
 Referenced in 37 articles
[sw40293]
 finds all frequent closed item sets in polynomial time per item set, without storing previously ... introduce several algorithmic techniques using the sparse and dense structures of input data. Algorithms...

DecomposableSparseSystems
 Referenced in 1 article
[sw36757]
 Macaulay2 package DecomposableSparseSystems  Solving decomposable sparse polynomial systems There are two natural ways a sparse ... polynomial system can be decomposed in the sense of (T.Brysiewicz, J.I.Rodriguez, F.Sottile, and T.Yahl, Solving ... Decomposable Sparse Systems, arXiv:2001.04228, 2019). These methods detect and compute these decompositions...

ffmodstd
 Referenced in 5 articles
[sw27228]
 Groebner basis of an ideal in a polynomial ring over an algebraic function field ... using modular methods and sparse multivariate rational interpolation, where the t_i are transcendental over ... obtain a set of polynomials G by applying the sparse multivariate rational interpolation algorithm from ... makes use of the following algorithms: univariate polynomial interpolation [2], univariate rational function reconstruction...

NSWC
 Referenced in 11 articles
[sw09119]
 functions, polynomials, vectors, matrices, large dense systems of linear equations, banded matrices, sparse matrices, eigenvalues...

MARS
 Referenced in 5 articles
[sw00549]
 implementation issues. The polynomial system is reduced to a sparse eigenvalue problem, using Sylvester/Macaulay...