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 280 articles , 1 standard article )

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  1. Capiński, Maciej J.; Mireles James, J.D.: Validated computation of heteroclinic sets (2017)
  2. Choi, Sou-Cheng T.; Ding, Yuhan; Hickernell, Fred J.; Tong, Xin: Local adaption for approximation and minimization of univariate functions (2017)
  3. Mizuguchi, Makoto; Takayasu, Akitoshi; Kubo, Takayuki; Oishi, Shin’ichi: A method of verified computations for solutions to semilinear parabolic equations using semigroup theory (2017)
  4. Pacella, Filomena; Plum, Michael; Rütters, Dagmar: A computer-assisted existence proof for Emden’s equation on an unbounded $L$-shaped domain (2017)
  5. Schichl, Hermann; Domes, Ferenc; Montanher, Tiago; Kofler, Kevin: Interval unions (2017)
  6. van den Berg, Jan Bouwe; Williams, J.F.: Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem (2017)
  7. Wanner, Thomas: Computer-assisted equilibrium validation for the diblock copolymer model (2017)
  8. Adam, Stavros P.; Magoulas, George D.; Karras, Dimitrios A.; Vrahatis, Michael N.: Bounding the search space for global optimization of neural networks learning error: an interval analysis approach (2016)
  9. Barker, Blake; Zumbrun, Kevin: Numerical proof of stability of viscous shock profiles (2016)
  10. Chen, Yunkun; Shi, Xinghua; Wei, Yimin: Convergence of Rump’s method for computing the Moore-Penrose inverse. (2016)
  11. Dehghani-Madiseh, Marzieh; Dehghan, Mehdi: Parametric AE-solution sets to the parametric linear systems with multiple right-hand sides and parametric matrix equation $A(p)X=B(p)$ (2016)
  12. de la Llave, R.; Mireles James, J.D.: Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence (2016)
  13. Eichfelder, Gabriele; Gerlach, Tobias; Sumi, Susanne: A modification of the $\alpha \mathrmBB$ method for box-constrained optimization and an application to inverse kinematics (2016)
  14. Elishakoff, Isaac; Gabriele, Stefano; Wang, Yan: Generalized galileo Galilei problem in interval setting for functionally related loads (2016) ioport
  15. Gameiro, Marcio; Lessard, Jean-Philippe; Pugliese, Alessandro: Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions (2016)
  16. Hladík, Milan: An extension of the $\alpha\mathrmBB$-type underestimation to linear parametric Hessian matrices (2016)
  17. Lessard, Jean-Philippe: Rigorous verification of saddle-node bifurcations in ODEs (2016)
  18. Sander, Evelyn; Wanner, Thomas: Validated saddle-node bifurcations and applications to lattice dynamical systems (2016)
  19. Watanabe, Yoshitaka: An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid (2016)
  20. Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.: Norm bound computation for inverses of linear operators in Hilbert spaces (2016)

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