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 373 articles , 1 standard article )

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  1. Breden, Maxime; Kuehn, Christian: Rigorous validation of stochastic transition paths (2019)
  2. Chousionis, Vasileios; Leykekhman, Dmitriy; Urbański, Mariusz: The dimension spectrum of conformal graph directed Markov systems (2019)
  3. Galván, Manuel López: The multivariate bisection algorithm (2019)
  4. Goldsztejn, Alexandre; Chabert, Gilles: Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation (2019)
  5. Hashimoto, Kouji; Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.: Constructive error analysis of a full-discrete finite element method for the heat equation (2019)
  6. Higham, Nicholas J.; Pranesh, Srikara: Simulating low precision floating-point arithmetic (2019)
  7. Hou, Guoliang; Zhang, Shugong: An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator (2019)
  8. Jaquette, Jonathan: A proof of Jones’ conjecture (2019)
  9. Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.: An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces (2019)
  10. Liao, Shih-Kang; Shu, Yu-Chen; Liu, Xuefeng: Optimal estimation for the Fujino-Morley interpolation error constants (2019)
  11. Miyajima, Shinya: Verified computation for the Hermitian positive definite solution of the conjugate discrete-time algebraic Riccati equation (2019)
  12. Miyajima, Shinya: Verified computation for the matrix principal logarithm (2019)
  13. Miyajima, Shinya: Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations (2019)
  14. Miyajima, Shinya: Verified computation of the matrix exponential (2019)
  15. Mohaghegh Tabar, Maryam; Keyanpour, Mohammad; Lodwick, Weldon A.: Solving interval linear programming problems with equality constraints using extended interval enclosure solutions (2019)
  16. Nagatou, K.; Plum, M.; McKenna, P. J.: Orbital stability investigations for travelling waves in a nonlinearly supported beam (2019)
  17. Niebling, Julia; Eichfelder, Gabriele: A branch-and-bound-based algorithm for nonconvex multiobjective optimization (2019)
  18. Reinhardt, Christian; Mireles James, J. D.: Fourier-Taylor parameterization of unstable manifolds for parabolic partial differential equations: formalism, implementation and rigorous validation (2019)
  19. Takayasu, Akitoshi; Yoon, Suro; Endo, Yasunori: Rigorous numerical computations for 1D advection equations with variable coefficients (2019)
  20. van den Berg, Jan Bouwe; Williams, J. F.: Rigorously computing symmetric stationary states of the Ohta-Kawasaki problem in three dimensions (2019)

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