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 255 articles , 1 standard article )

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  1. 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)
  2. de la Llave, R.; Mireles James, J.D.: Connecting orbits for compact infinite dimensional maps: computer assisted proofs of existence (2016)
  3. Eichfelder, Gabriele; Gerlach, Tobias; Sumi, Susanne: A modification of the $\alpha \mathrmBB$ method for box-constrained optimization and an application to inverse kinematics (2016)
  4. Gameiro, Marcio; Lessard, Jean-Philippe; Pugliese, Alessandro: Computation of smooth manifolds via rigorous multi-parameter continuation in infinite dimensions (2016)
  5. Hladík, Milan: An extension of the $\alpha\mathrmBB$-type underestimation to linear parametric Hessian matrices (2016)
  6. Sander, Evelyn; Wanner, Thomas: Validated saddle-node bifurcations and applications to lattice dynamical systems (2016)
  7. Watanabe, Yoshitaka: An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid (2016)
  8. Watanabe, Yoshitaka; Nagatou, Kaori; Plum, Michael; Nakao, Mitsuhiro T.: Norm bound computation for inverses of linear operators in Hilbert spaces (2016)
  9. Birrell, Jeremiah: A posteriori error bounds for two point boundary value problems: a Green’s function approach (2015)
  10. Cai, Shuting; Watanabe, Yoshitaka: A computer-assisted method for excluding eigenvalues of an elliptic operator linearized at a solution of a nonlinear problem (2015)
  11. Castelli, Roberto: The monotonicity of the apsidal angle in power-law potential systems (2015)
  12. Castelli, Roberto; Lessard, Jean-Philippe; Mireles James, Jason D.: Analytic enclosure of the fundamental matrix solution. (2015)
  13. Cui, Yan; An, Ruxiao; Ariyur, Kartik B.: Cellphone geolocation via magnetic mapping (2015)
  14. D’Ambrosio, Lorenzo; Lessard, Jean-Philippe; Pugliese, Alessandro: Blow-up profile for solutions of a fourth order nonlinear equation (2015)
  15. Estévez Schwarz, Diana; Lamour, René: Diagnosis of singular points of structured DAEs using automatic differentiation (2015)
  16. Ewald, T.; Reif, U.; Sabin, M.: Hölder regularity of geometric subdivision schemes (2015)
  17. Hanapiah, Nur Lin Mohd; Monsi, Mansor; Hassan, Nasruddin; Ali, Fadzilah Md: Interval total single step procedure for bounding polynomial zeros (2015)
  18. Hladík, Milan: On the efficient Gerschgorin inclusion usage in the global optimization $\alpha$BB method (2015)
  19. Jamaludin, Nur Alif Akid; Monsi, Mansor; Hassan, Nasruddin: The Newton’s method interval single-step procedure for bounding polynomial zeros simultaneously (2015)
  20. Kearfott, Ralph Baker: Some observations on exclusion regions in branch and bound algorithms (2015)

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