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 407 articles , 1 standard article )

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  1. Yamamoto, Nobito; Genma, Kenta: On error estimation of finite element approximations to the elliptic equations in nonconvex polygonal domains (2007)
  2. Becuwe, Stefan; Cuyt, Annie: On the fast solution of Toeplitz-block linear systems arising in multivariate approximation theory (2006)
  3. Bornemann, Folkmar; Laurie, Dirk; Wagon, Stan; Waldvogel, Jörg: The SIAM 100-Digit Challenge: a study in high-accuracy numerical computing. With Foreword by David H. Bailey. Translated from the English. (2006)
  4. Kolev, Lubomir V.: Outer interval solution of the eigenvalue problem under general form parametric dependencies (2006)
  5. Lordelo, Alfredo D. S.; Juzzo, Edvaldo A.; Ferreira, Paulo A. V.: Analysis and design of robust controllers using the interval Diophantine equation (2006)
  6. Mayer, Günter: A contribution to the feasibility of the interval Gaussian algorithm (2006)
  7. Messine, Frédéric; Touhami, Ahmed: A general reliable quadratic form: An extension of affine arithmetic (2006)
  8. Pryce, J. D.; Corliss, G. F.: Interval arithmetic with containment sets (2006)
  9. Rump, Siegfried M.: Eigenvalues, pseudospectrum and structured perturbations (2006)
  10. Rump, S. M.: Verification of positive definiteness (2006)
  11. Schön, S.; Kutterer, H.: Uncertainty in GPS networks due to remaining systematic errors: the interval approach (2006)
  12. Zhang, Xian; Cai, Jianfeng; Wei, Yimin: Interval iterative methods for computing Moore-Penrose inverse (2006)
  13. Alefeld, Götz; Mayer, Günter: Enclosing solutions of singular interval systems iteratively (2005)
  14. Hashimoto, Kouji; Abe, Ryohei; Nakao, Mitsuhiro T.; Watanabe, Yoshitaka: A numerical verification method for solutions of singularly perturbed problems with nonlinearity (2005)
  15. Hashimoto, Kouji; Kobayashi, Kenta; Nakao, Mitsuhiro T.: Numerical verification methods for solutions of the free boundary problem (2005)
  16. Moore, Kevin L.; Chen, Yangquan; Bahl, Vikas: Monotonically convergent iterative learning control for linear discrete-time systems (2005)
  17. Nakao, M. T.; Hashimoto, K.; Watanabe, Y.: A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems (2005)
  18. Ogita, Takeshi; Oishi, Shin’ichi: Fast inclusion of interval matrix multiplication (2005)
  19. Ogita, Takeshi; Rump, Siegfried M.; Oishi, Shin’ichi: Accurate sum and dot product (2005)
  20. Revol, Nathalie; Rouillier, Fabrice: Motivations for an arbitrary precision interval arithmetic and the MPFI library (2005)

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