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 385 articles , 1 standard article )

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  1. Bünger, Florian: A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB (2020)
  2. Imakura, Akira; Morikuni, Keiichi; Takayasu, Akitoshi: Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems (2020)
  3. Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.: Constructive error estimates for full discrete approximation of periodic solution for heat equation (2020)
  4. Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.: Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space (2020)
  5. Minamihata, Atsushi; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi: Modified error bounds for approximate solutions of dense linear systems (2020)
  6. Stanimirović, Predrag S.; Roy, Falguni; Gupta, Dharmendra K.; Srivastava, Shwetabh: Computing the Moore-Penrose inverse using its error bounds (2020)
  7. Breden, Maxime; Kuehn, Christian: Rigorous validation of stochastic transition paths (2019)
  8. Chousionis, Vasileios; Leykekhman, Dmitriy; Urbański, Mariusz: The dimension spectrum of conformal graph directed Markov systems (2019)
  9. Dai, Liyun; Fan, Zhe; Xia, Bican; Zhang, Hanwen: Logcf: an efficient tool for real root isolation (2019)
  10. Galván, Manuel López: The multivariate bisection algorithm (2019)
  11. Goldsztejn, Alexandre; Chabert, Gilles: Estimating the robust domain of attraction for non-smooth systems using an interval Lyapunov equation (2019)
  12. Hashimoto, Kouji; Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.: Constructive error analysis of a full-discrete finite element method for the heat equation (2019)
  13. Higham, Nicholas J.; Pranesh, Srikara: Simulating low precision floating-point arithmetic (2019)
  14. Hou, Guoliang; Zhang, Shugong: An improved verification algorithm for nonlinear systems of equations based on Krawczyk operator (2019)
  15. Ivanov, Ivan G.; Mateva, Tonya: Interval methods with fifth order of convergence for solving nonlinear scalar equations (2019)
  16. Jaquette, Jonathan: A proof of Jones’ conjecture (2019)
  17. Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.: An alternative approach to norm bound computation for inverses of linear operators in Hilbert spaces (2019)
  18. Liao, Shih-Kang; Shu, Yu-Chen; Liu, Xuefeng: Optimal estimation for the Fujino-Morley interpolation error constants (2019)
  19. Miyajima, Shinya: Verified computation of the matrix exponential (2019)
  20. Miyajima, Shinya: Robust verification algorithm for stabilizing solutions of discrete-time algebraic Riccati equations (2019)

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