INTLAB

INTLAB is the Matlab toolbox for reliable computing and self-validating algorithms. It comprises of self-validating methods for dense linear systems (also inner inclusions and structured matrices) sparse s.p.d. linear systems systems of nonlinear equations (including unconstrained optimization) roots of univariate and multivariate nonlinear equations (simple and clusters) eigenvalue problems (simple and clusters, also inner inclusions and structured matrices) generalized eigenvalue problems (simple and clusters) quadrature for univariate functions univariate polynomial zeros (simple and clusters) interval arithmetic for real and complex data including vectors and matrices (very fast) interval arithmetic for real and complex sparse matrices (very fast) automatic differentiation (forward mode, vectorized computations, fast) Gradients (to solve systems of nonlinear equations) Hessians (for global optimization) Taylor series for univariate functions automatic slopes (sequential approach, slow for many variables) verified integration of (simple) univariate functions univariate and multivariate (interval) polynomials rigorous real interval standard functions (fast, very accurate,  3 ulps) rigorous complex interval standard functions (fast, rigorous, but not necessarily sharp inclusions) rigorous input/output (outer and inner inclusions) accurate summation, dot product and matrix-vector residuals (interpreted, reference implementation, slow) multiple precision interval arithmetic with error bounds (does the job, slow)


References in zbMATH (referenced in 446 articles , 1 standard article )

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  1. Asai, Taisei; Tanaka, Kazuaki; Oishi, Shin’ichi: Numerical verification for asymmetric solutions of the Hénon equation on bounded domains (2022)
  2. Cai, Shuting; Watanabe, Yoshitaka: Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem (2021)
  3. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  4. Carrizosa, Emilio; Messine, Frédéric: An interval branch and bound method for global robust optimization (2021)
  5. Church, Kevin E. M.: Analysis of pandemic closing-reopening cycles using rigorous homotopy continuation: a case study with Montreal COVID-19 data (2021)
  6. Church, Kevin E. M.; Fortin, Clément: Computer-assisted methods for analyzing periodic orbits in vibrating gravitational billiards (2021)
  7. Eichfelder, Gabriele; Kirst, Peter; Meng, Laura; Stein, Oliver: A general branch-and-bound framework for continuous global multiobjective optimization (2021)
  8. Eichfelder, Gabriele; Klamroth, Kathrin; Niebling, Julia: Nonconvex constrained optimization by a filtering branch and bound (2021)
  9. Füllner, Christian; Kirst, Peter; Stein, Oliver: Convergent upper bounds in global minimization with nonlinear equality constraints (2021)
  10. Lange, Marko; Rump, Siegfried M.: Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s (\sin(\theta)) theorem (2021)
  11. Liu, Xuefeng; Nakao, Mitsuhiro T.; You, Chun’guang; Oishi, Shin’ichi: Explicit a posteriori and a priori error estimation for the finite element solution of Stokes equations (2021)
  12. Miyajima, Shinya: Verified computation for the geometric mean of two matrices (2021)
  13. Miyajima, Shinya: Fast verification for the Perron pair of an irreducible nonnegative matrix (2021)
  14. Miyajima, Shinya: Verified computation of real powers of matrices (2021)
  15. Miyajima, Shinya: Computing enclosures for the matrix Mittag-Leffler function (2021)
  16. Reif, Ulrich; Weinmann, Andreas: Clothoid fitting and geometric Hermite subdivision (2021)
  17. Sander, Evelyn; Wanner, Thomas: Equilibrium validation in models for pattern formation based on Sobolev embeddings (2021)
  18. Titi, Jihad; Garloff, Jürgen: Bounds for the range of a complex polynomial over a rectangular region (2021)
  19. van den Berg, Jan Bouwe; Breden, Maxime; Lessard, Jean-Philippe; van Veen, Lennaert: Spontaneous periodic orbits in the Navier-Stokes flow (2021)
  20. van den Berg, Jan Bouwe; Queirolo, Elena: A general framework for validated continuation of periodic orbits in systems of polynomial ODEs (2021)

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