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 298 articles , 1 standard article )

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  1. Miyajima, Shinya: Fast verified computation for the matrix principal $p$th root (2018)
  2. Capiński, Maciej J.; Mireles James, J.D.: Validated computation of heteroclinic sets (2017)
  3. Choi, Sou-Cheng T.; Ding, Yuhan; Hickernell, Fred J.; Tong, Xin: Local adaption for approximation and minimization of univariate functions (2017)
  4. Fendl, Hannes; Neumaier, Arnold; Schichl, Hermann: Certificates of infeasibility via nonsmooth optimization (2017)
  5. Jaquette, Jonathan; Lessard, Jean-Philippe; Mischaikow, Konstantin: Stability and uniqueness of slowly oscillating periodic solutions to Wright’s equation (2017)
  6. Kobayashi, Ryo; Kimura, Takuma; Oishi, Shin’ichi: A method for verifying the accuracy of numerical solutions of symmetric saddle point linear systems (2017)
  7. Matsue, Kaname; Hiwaki, Tomohiro; Yamamoto, Nobito: On the construction of Lyapunov functions with computer assistance (2017)
  8. Mitrea, Irina; Ott, Katharine; Tucker, Warwick: Invertibility properties of singular integral operators associated with the Lamé and Stokes systems on infinite sectors in two dimensions (2017)
  9. Miyajima, Shinya: Fast verified computation for stabilizing solutions of discrete-time algebraic Riccati equations (2017)
  10. Mizuguchi, Makoto; Takayasu, Akitoshi; Kubo, Takayuki; Oishi, Shin’ichi: Numerical verification for existence of a global-in-time solution to semilinear parabolic equations (2017)
  11. Mizuguchi, Makoto; Takayasu, Akitoshi; Kubo, Takayuki; Oishi, Shin’ichi: A method of verified computations for solutions to semilinear parabolic equations using semigroup theory (2017)
  12. Pacella, Filomena; Plum, Michael; Rütters, Dagmar: A computer-assisted existence proof for Emden’s equation on an unbounded $L$-shaped domain (2017)
  13. Schichl, Hermann; Domes, Ferenc; Montanher, Tiago; Kofler, Kevin: Interval unions (2017)
  14. Tanaka, Kazuaki; Sekine, Kouta; Mizuguchi, Makoto; Oishi, Shin’ichi: Sharp numerical inclusion of the best constant for embedding $H_0^1(\Omega) \hookrightarrow L^p(\Omega)$ on bounded convex domain (2017)
  15. van den Berg, Jan Bouwe; Williams, J.F.: Validation of the bifurcation diagram in the 2D Ohta-Kawasaki problem (2017)
  16. Wanner, Thomas: Computer-assisted equilibrium validation for the diblock copolymer model (2017)
  17. 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)
  18. Barker, Blake; Zumbrun, Kevin: Numerical proof of stability of viscous shock profiles (2016)
  19. Chen, Yunkun; Shi, Xinghua; Wei, Yimin: Convergence of Rump’s method for computing the Moore-Penrose inverse. (2016)
  20. 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)

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