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 407 articles , 1 standard article )

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  1. Niebling, Julia; Eichfelder, Gabriele: A branch-and-bound-based algorithm for nonconvex multiobjective optimization (2019)
  2. Reinhardt, Christian; Mireles James, J. D.: Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation (2019)
  3. Takayasu, Akitoshi; Yoon, Suro; Endo, Yasunori: Rigorous numerical computations for 1D advection equations with variable coefficients (2019)
  4. van den Berg, Jan Bouwe; Williams, J. F.: Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions (2019)
  5. Wang, Yu; Xia, Bican: A hybrid procedure for finding real points on a real algebraic set (2019)
  6. Watanabe, Yoshitaka; Kinoshita, Takehiko; Nakao, Mitsuhiro T.: An improved method for verifying the existence and bounds of the inverse of second-order linear elliptic operators mapping to dual space (2019)
  7. You, Chun’Guang; Xie, Hehu; Liu, Xuefeng: Guaranteed eigenvalue bounds for the Steklov eigenvalue problem (2019)
  8. Balázs, István; van den Berg, Jan Bouwe; Courtois, Julien; Dudás, János; Lessard, Jean-Philippe; Vörös-Kiss, Anett; Williams, J. F.; Yin, Xi Yuan: Computer-assisted proofs for radially symmetric solutions of PDEs (2018)
  9. Baydin, Atılım Güneş; Pearlmutter, Barak A.; Radul, Alexey Andreyevich; Siskind, Jeffrey Mark: Automatic differentiation in machine learning: a survey (2018)
  10. Boeck, Thomas; Terzijska, Džulia; Eichfelder, Gabriele: Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles (2018)
  11. Breden, Maxime; Castelli, Roberto: Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof (2018)
  12. Breden, Maxime; Lessard, Jean-Philippe: Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs (2018)
  13. Bünger, Florian: Shrink wrapping for Taylor models revisited (2018)
  14. Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe: Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation (2018)
  15. Castelli, Roberto; Garrione, Maurizio: Some unexpected results on the Brillouin singular equation: fold bifurcation of periodic solutions (2018)
  16. Dehghani-Madiseh, Marzieh; Hladík, Milan: Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations (2018)
  17. Eftekhari, Tahereh: Interval extension of the three-step Kung and Traub’s method (2018)
  18. Ghanbari, Mojtaba: An estimation of algebraic solution for a complex interval linear system (2018)
  19. Goluskin, David: Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system (2018)
  20. Haqiri, Tayyebe; Mohseni Moghadam, Mahmoud; Rivaz, Azim: The united stable solution set of interval continuous-time algebraic Riccati equation and verified numerical computation of its outer estimation (2018)

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