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 471 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. Church, Kevin E. M.; Duchesne, Gabriel William: Rigorous continuation of periodic solutions for impulsive delay differential equations (2022)
  3. Constantineau, Kevin; García-Azpeitia, Carlos; Lessard, Jean-Philippe: Spatial relative equilibria and periodic solutions of the Coulomb ((n+1))-body problem (2022)
  4. Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi: Global dynamics in nonconservative nonlinear Schrödinger equations (2022)
  5. Jaquette, Jonathan; Lessard, Jean-Philippe; Takayasu, Akitoshi: Singularities and heteroclinic connections in complex-valued evolutionary equations with a quadratic nonlinearity (2022)
  6. Liu, Xuefeng; Nakao, Mitsuhiro T.; Oishi, Shin’ichi: Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains (2022)
  7. Li, Zhe; Zhang, Chunlei: The verification of multiplicity support of a defective eigenvalue of a real matrix (2022)
  8. Miyajima, Shinya: Verified computation of matrix gamma function (2022)
  9. Miyajima, Shinya: Fast verified computation for positive solutions to (\mathcalM)-tensor multi-linear systems and Perron vectors of a kind of weakly irreducible nonnegative tensors (2022)
  10. Mrozek, Marian; Srzednicki, Roman; Thorpe, Justin; Wanner, Thomas: Combinatorial vs. classical dynamics: recurrence (2022)
  11. Nitta, Koki; Yamamoto, Nobito; Matsue, Kaname: A numerical verification method to specify homoclinic orbits as application of local Lyapunov functions (2022)
  12. Tanaka, Kazuaki; Asai, Taisei: A posteriori verification of the positivity of solutions to elliptic boundary value problems (2022)
  13. Tanaka, Kazuaki; Plum, Michael; Sekine, Kouta; Kashiwagi, Masahide; Oishi, Shin’ichi: Rigorous numerical enclosures for positive solutions of Lane-Emden’s equation with sub-square exponents (2022)
  14. van den Berg, Jan Bouwe; Groothedde, Chris; Lessard, Jean-Philippe: A general method for computer-assisted proofs of periodic solutions in delay differential problems (2022)
  15. van den Berg, Jan Bouwe; Queirolo, Elena: Rigorous validation of a Hopf bifurcation in the Kuramoto-Sivashinsky PDE (2022)
  16. Breden, Maxime; Chainais-Hillairet, Claire; Zurek, Antoine: Existence of traveling wave solutions for the diffusion Poisson coupled model: a computer-assisted proof (2021)
  17. Cai, Shuting; Watanabe, Yoshitaka: Computer-assisted proofs of the existence of a symmetry-breaking bifurcation point for the Kolmogorov problem (2021)
  18. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  19. Carrizosa, Emilio; Messine, Frédéric: An interval branch and bound method for global robust optimization (2021)
  20. Church, Kevin E. M.: Eigenvalues and delay differential equations: periodic coefficients, impulses and rigorous numerics (2021)

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