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 435 articles , 1 standard article )

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  1. Calleja, Renato; García-Azpeitia, Carlos; Lessard, Jean-Philippe; Mireles James, J. D.: Torus knot choreographies in the (n)-body problem (2021)
  2. Füllner, Christian; Kirst, Peter; Stein, Oliver: Convergent upper bounds in global minimization with nonlinear equality constraints (2021)
  3. Lange, Marko; Rump, Siegfried M.: Verified inclusions for a nearest matrix of specified rank deficiency via a generalization of Wedin’s (\sin(\theta)) theorem (2021)
  4. Miyajima, Shinya: Computing enclosures for the matrix Mittag-Leffler function (2021)
  5. Miyajima, Shinya: Verified computation for the geometric mean of two matrices (2021)
  6. Miyajima, Shinya: Verified computation of real powers of matrices (2021)
  7. Sander, Evelyn; Wanner, Thomas: Equilibrium validation in models for pattern formation based on Sobolev embeddings (2021)
  8. Titi, Jihad; Garloff, Jürgen: Bounds for the range of a complex polynomial over a rectangular region (2021)
  9. van den Berg, Jan Bouwe; Breden, Maxime; Lessard, Jean-Philippe; van Veen, Lennaert: Spontaneous periodic orbits in the Navier-Stokes flow (2021)
  10. van den Berg, Jan Bouwe; Queirolo, Elena: A general framework for validated continuation of periodic orbits in systems of polynomial ODEs (2021)
  11. Yamamura, Kiyotaka: An efficient algorithm for finding all solutions of nonlinear equations using parallelogram LP test (2021)
  12. Alama, Yvonne Bronsard; Lessard, Jean-Philippe: Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption (2020)
  13. Aurentz, Jared L.; Hashemi, Behnam: The Laurent-Horner method for validated evaluation of Chebyshev expansions (2020)
  14. Bajaj, Ishan; Hasan, M. M. Faruque: Global dynamic optimization using edge-concave underestimator (2020)
  15. Bánhelyi, Balázs; Csendes, Tibor; Hatvani, László: On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum (2020)
  16. Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore: Interval tensors and their application in solving multi-linear systems of equations (2020)
  17. Bünger, Florian: A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB (2020)
  18. Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi: A new deflation method for verifying the isolated singular zeros of polynomial systems (2020)
  19. Eftekhari, Tahereh: Interval extensions of the Halley method and its modified method for finding enclosures of roots of nonlinear equations (2020)
  20. Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan: An algorithmic approach to multiobjective optimization with decision uncertainty (2020)

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