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 406 articles , 1 standard article )

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  1. Faragó, I.; Palencia, C.: Sharpening the estimate of the stability constant in the maximum-norm of the Crank-Nicolson scheme for the one-dimensional heat equation (2002)
  2. Huhtanen, Marko; Larsen, Rasmus Munk: Exclusion and inclusion regions for the eigenvalues of a normal matrix (2002)
  3. Kulisch, Ulrich W.: Advanced artihmetic for the digital computer. Design of arithmetic units (2002)
  4. Nataraj, Paluri S. V.; Sheela, Suresh Mandir: A new subdivision strategy for range computations (2002)
  5. Nataraj, P. S. V.: Interval QFT: A mathematical and computational enhancement of QFT (2002)
  6. Neumaier, Arnold: Grand challenges and scientific standards in interval analysis (2002)
  7. Papamichail, Ioannis; Adjiman, Claire S.: A rigorous global optimization algorithm for problems with ordinary differential equations (2002)
  8. Ryoo, C. S.; Agarwal, R. P.: Numerical inclusion methods of solutions for variational inequalities (2002)
  9. Sakurai, Tetsuya; Sugiura, Hiroshi: Improvement of convergence of an iterative method for finding polynomial factors of analytic functions (2002)
  10. Toyonaga, K.; Nakao, M. T.; Watanabe, Y.: Verified numerical computations for multiple and nearly multiple eigenvalues of elliptic operators (2002)
  11. Alt, Rene; Markov, Svetoslav: On the algebraic properties of stochastic arithmetic. Comparison to interval arithmetic (2001)
  12. Chen, Xiaojun; Shogenji, Yukihiro; Yamasaki, Maretsugu: Verification for existence of solutions of linear complementarity problems (2001)
  13. Heeks, Jürgen; Hofer, Eberhard P.; Tibken, Bernd; Lunde, Karin; Thorwart, Klaus: Simulation of a controlled aircraft elevator under sensor uncertainties (2001)
  14. Jansson, Christian: Quasiconvex relaxations based on interval arithmetic (2001)
  15. Jaulin, Luc; Kieffer, Michel; Didrit, Olivier; Walter, Éric: Applied interval analysis. With examples in parameter and state estimation, robust control and robotics. Incl. 1 CD-ROM (2001)
  16. Markov, Svetoslav: Computation of algebraic solutions to interval systems via systems of coordinates (2001)
  17. Rump, Siegfried M.: Self-validating methods (2001)
  18. Rump, Siegfried M.: Rigorous and portable standard functions (2001)
  19. Rump, Siegfried M.: Fast verification algorithms in Matlab (2001)
  20. Rump, Siegfried M.: Computational error bounds for multiple or nearly multiple eigenvalues (2001)

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