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 419 articles , 1 standard article )

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  1. Yamamura, Kiyotaka: An efficient algorithm for finding all solutions of nonlinear equations using parallelogram LP test (2021)
  2. Alama, Yvonne Bronsard; Lessard, Jean-Philippe: Traveling wave oscillatory patterns in a signed Kuramoto-Sivashinsky equation with absorption (2020)
  3. Aurentz, Jared L.; Hashemi, Behnam: The Laurent-Horner method for validated evaluation of Chebyshev expansions (2020)
  4. Bajaj, Ishan; Hasan, M. M. Faruque: Global dynamic optimization using edge-concave underestimator (2020)
  5. Bánhelyi, Balázs; Csendes, Tibor; Hatvani, László: On the existence and stabilization of an upper unstable limit cycle of the damped forced pendulum (2020)
  6. Bozorgmanesh, Hassan; Hajarian, Masoud; Chronopoulos, Anthony Theodore: Interval tensors and their application in solving multi-linear systems of equations (2020)
  7. Bünger, Florian: A Taylor model toolbox for solving ODEs implemented in Matlab/INTLAB (2020)
  8. Cheng, Jin-San; Dou, Xiaojie; Wen, Junyi: A new deflation method for verifying the isolated singular zeros of polynomial systems (2020)
  9. Eichfelder, Gabriele; Niebling, Julia; Rocktäschel, Stefan: An algorithmic approach to multiobjective optimization with decision uncertainty (2020)
  10. Hashimoto, Kouji; Kinoshita, Takehiko; Nakao, Mitsuhiro T.: Numerical verification of solutions for nonlinear parabolic problems (2020)
  11. Hoshi, Takeo; Ogita, Takeshi; Ozaki, Katsuhisa; Terao, Takeshi: An a posteriori verification method for generalized real-symmetric eigenvalue problems in large-scale electronic state calculations (2020)
  12. Imakura, Akira; Morikuni, Keiichi; Takayasu, Akitoshi: Verified partial eigenvalue computations using contour integrals for Hermitian generalized eigenproblems (2020)
  13. Kimura, Takuma; Minamoto, Teruya; Nakao, Mitsuhiro T.: Constructive error estimates for full discrete approximation of periodic solution for heat equation (2020)
  14. Kinoshita, Takehiko; Watanabe, Yoshitaka; Nakao, Mitsuhiro T.: Some lower bound estimates for resolvents of a compact operator on an infinite-dimensional Hilbert space (2020)
  15. Lange, Marko; Rump, Siegfried M.: Faithfully rounded floating-point computations (2020)
  16. Lessard, J. P.; Mireles James, J. D.: A functional analytic approach to validated numerics for eigenvalues of delay equations (2020)
  17. Liu, Xuefeng: Explicit eigenvalue bounds of differential operators defined by symmetric positive semi-definite bilinear forms (2020)
  18. Minamihata, Atsushi; Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi: Modified error bounds for approximate solutions of dense linear systems (2020)
  19. Miyajima, Shinya: Enclosing Moore-Penrose inverses (2020)
  20. Nigam, Nilima; Siudeja, Bartłomiej; Young, Benjamin: A proof via finite elements for Schiffer’s conjecture on a regular pentagon (2020)

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