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 330 articles , 1 standard article )

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  1. Boeck, Thomas; Terzijska, Džulia; Eichfelder, Gabriele: Maximum electromagnetic drag configurations for a translating conducting cylinder with distant magnetic dipoles (2018)
  2. Breden, Maxime; Castelli, Roberto: Existence and instability of steady states for a triangular cross-diffusion system: a computer-assisted proof (2018)
  3. Breden, Maxime; Lessard, Jean-Philippe: Polynomial interpolation and a priori bootstrap for computer-assisted proofs in nonlinear ODEs (2018)
  4. Bünger, Florian: Shrink wrapping for Taylor models revisited (2018)
  5. Castelli, Roberto; Gameiro, Marcio; Lessard, Jean-Philippe: Rigorous numerics for ill-posed PDEs: periodic orbits in the Boussinesq equation (2018)
  6. Castelli, Roberto; Garrione, Maurizio: Some unexpected results on the Brillouin singular equation: fold bifurcation of periodic solutions (2018)
  7. Dehghani-Madiseh, Marzieh; Hladík, Milan: Efficient approaches for enclosing the united solution set of the interval generalized Sylvester matrix equations (2018)
  8. Ghanbari, Mojtaba: An estimation of algebraic solution for a complex interval linear system (2018)
  9. Goluskin, David: Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system (2018)
  10. Hladík, Milan: Testing pseudoconvexity via interval computation (2018)
  11. Kalies, William D.; Kepley, Shane; Mireles James, J. D.: Analytic continuation of local (un)stable manifolds with rigorous computer assisted error bounds (2018)
  12. Kazazakis, N.; Adjiman, C. S.: Arbitrarily tight $\alpha \mathrmBB$ underestimators of general non-linear functions over sub-optimal domains (2018)
  13. Li, Zhe; Wan, Baocheng; Gao, Ruimei: Verified error bounds for eigenvalues of geometric multiplicity $q$ and corresponding invariant subspaces (2018)
  14. Miyajima, Shinya: Fast verified computation for the solvent of the quadratic matrix equation (2018)
  15. Miyajima, Shinya: Fast verified computation for the matrix principal $p$th root (2018)
  16. Muller, Jean-Michel; Brunie, Nicolas; de Dinechin, Florent; Jeannerod, Claude-Pierre; Joldes, Mioara; Lefèvre, Vincent; Melquiond, Guillaume; Revol, Nathalie; Torres, Serge: Handbook of floating-point arithmetic (2018)
  17. Nepomuceno, Erivelton G.; Peixoto, Márcia L. C.; Martins, Samir A. M.; Rodrigues, Heitor M. Junior; Perc, Matjaž: Inconsistencies in numerical simulations of dynamical systems using interval arithmetic (2018)
  18. Roy, Falguni; Gupta, D. K.; Stanimirović, Predrag S.: An interval extension of SMS method for computing weighted Moore-Penrose inverse (2018)
  19. Rump, Siegfried M.: Mathematically rigorous global optimization in floating-point arithmetic (2018)
  20. van den Berg, Jan Bouwe; Breden, Maxime; Lessard, Jean-Philippe; Murray, Maxime: Continuation of homoclinic orbits in the suspension bridge equation: a computer-assisted proof (2018)

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