• alphaCertified

  • Referenced in 47 articles [sw07351]
  • Algorithm 921: alphaCertified: Certifying solutions to polynomial systems. Smale’s α-theory uses estimates related ... convergence of Newton’s method to certify that Newton iterations will converge quadratically to solutions ... program alphaCertified implements algorithms based on α-theory to certify solutions of polynomial systems using ... floating point arithmetic. It also implements algorithms that certify whether a given point corresponds...
  • Mathemagix

  • Referenced in 42 articles [sw00553]
  • scientific programming language for symbolic and certified numeric algorithms. This language can be compiled ... will illustrate possibilities offered for certified numeric computations with balls and intervals...
  • Berlekamp Zassenhaus

  • Referenced in 9 articles [sw28596]
  • thus provide an efficient and certified factorization algorithm for arbitrary univariate polynomials. The algorithm first...
  • SE-Sync

  • Referenced in 8 articles [sw40678]
  • Sync: A Certifiably Correct Algorithm for Synchronization over the Special Euclidean Group. Many important geometric ... present an algorithm that is able to efficiently recover certifiably globally optimal solutions ... verify this fact a posteriori, thereby certifying the optimality of the recovered estimate. We develop ... simple rounding procedure to produce our algorithm, SE-Sync. Experimental evaluation on a variety...
  • RationalFirstintegrals

  • Referenced in 6 articles [sw14472]
  • planar polynomial vector fields. We present fast algorithms for computing rational first integrals with bounded ... transform their method into a certified algorithm computing rational first integrals via systems of linear...
  • CAQE

  • Referenced in 12 articles [sw25922]
  • CAQE: a certifying QBF solver. We present a new CEGAR-based algorithm ... algorithm builds on a decomposition of QBFs into a sequence of propositional formulas, which ... allowing us to certify the solver result. We implemented the algorithm in a solver called ... current QBF solvers and outperforms previous certifying solvers...
  • Axel

  • Referenced in 22 articles [sw06457]
  • algorithms to compute intersection points or curves, singularities of algebraic curves or surfaces, certified topology...
  • HSPICE

  • Referenced in 12 articles [sw11821]
  • foundry-certified MOS device models with state-of-the-art simulation and analysis algorithms. With...
  • Optimal-SPCA

  • Referenced in 3 articles [sw31821]
  • Certifiably optimal sparse principal component analysis. This paper addresses the sparse principal component analysis (SPCA ... bound algorithm, Optimal-SPCA, that enables us to solve SPCA to certifiable optimality in seconds...
  • RookWalks

  • Referenced in 2 articles [sw11424]
  • challenge to develop algorithms which can also certify the correctness of the equations we found...
  • RealCertify

  • Referenced in 7 articles [sw28191]
  • RealCertify: a Maple package for certifying non-negativity. Let Q (resp. R) be the field ... constraints in Q[X] is a classical algorithmic problem for symbolic computation. The Maple package...
  • NLCertify

  • Referenced in 4 articles [sw08786]
  • Sollya environment, in which an iterative algorithm designed by Remez is implemented. Alternatively, the maxplus ... quadratic forms. In this way, NLCertify computes certified global estimators from approximations of primitive functions ... tree t. These various approximation and optimization algorithms are placed in a unified framework extending...
  • RBniCS

  • Referenced in 12 articles [sw33333]
  • reduced order modelling techniques (and, in particular, certified reduced basis method and Proper Orthogonal Decomposition ... reduced basis and proper orthogonal decomposition) and algorithms (such as successive constraint method, empirical interpolation...
  • Synthia

  • Referenced in 8 articles [sw12933]
  • partially implemented systems, in which case it certifies their realizability by synthesizing reference implementations ... arising infinite state space. Synthia’s analysis algorithm is based on a novel abstraction refinement...
  • FoCaLiZe

  • Referenced in 10 articles [sw12384]
  • providing a programming environment to develop certified programs. The environment is based on a functional ... noticeably efficient; for instance, the complex algorithms of the algebraic library provide runtime performances comparable...
  • FastCertRelPose

  • Referenced in 1 article [sw40676]
  • Fast and robust certifiable estimation of the relative pose between two calibrated cameras. This work ... efficient algorithm to compute the relative pose problem (RPp) between calibrated cameras and certify...
  • IML - Integer Matrix Library

  • Referenced in 16 articles [sw00440]
  • library of C source code which implements algorithms for computing exact solutions to dense systems ... right nullspace of an integer matrix. Certified linear system solving: compute a minimal denominator solution...
  • Axl

  • Referenced in 3 articles [sw25792]
  • defined by polynomial equations. Moreover, Axl provides algorithms for processing these geometric representations, such ... models, singularities of algebraic curves or surfaces, certified topology of curves and surfaces...
  • 3D spherical kernel

  • Referenced in 5 articles [sw11156]
  • sphere. We present a CGAL kernel for algorithms manipulating 3D spheres, circles, and circular arcs ... sample molecular models), it is shown that certifying the result incurs a modest factor...
  • Real_Impl

  • Referenced in 2 articles [sw29247]
  • this end, we also developed algorithms to precisely compute roots of a rational number ... factors. Our results have been used to certify termination proofs which involve polynomial interpretations over...