INTLAB

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. Sommese, Andrew J.; Wampler, Charles W. II: The numerical solution of systems of polynomials. Arising in engineering and science. (2005)
  2. Verdonk, B.; Vervloet, J.; Cuyt, A.: Blending set and interval arithmetic for maximal reliability (2005)
  3. Corliss, George F.; Yu, Jun: Interval testing strategies applied to COSY’s interval and Taylor model arithmetic (2004)
  4. Grimmer, Markus; Petras, Knut; Revol, Nathalie: Multiple precision interval packages: comparing different approaches (2004)
  5. Hofschuster, Werner; Krämer, Walter: C-XSC 2.0 -- a C++ library for extended scientific computing (2004)
  6. Kearfott, R. Baker; Neher, Markus; Oishi, Shin’ichi; Rico, Fabien: Libraries, tools, and interactive systems for verified computations four case studies (2004)
  7. Malyshev, A. N.; Sadkane, M.: Componentwise pseudospectrum of a matrix (2004)
  8. Ryoo, Cheon Seoung: A numerical verification of solutions of free boundary problems (2004)
  9. Schichl, Hermann; Neumaier, Arnold: Exclusion regions for systems of equations (2004)
  10. Eble, Ingo; Neher, Markus: ACETAF: A software package for computing validated bounds for Taylor coefficients of analytic functions (2003)
  11. Kulpa, Z.; Markov, S.: On the inclusion properties of interval multiplication: A diagrammatic study (2003)
  12. Makino, Kyoko; Berz, Martin: Taylor models and other validated functional inclusion methods (2003)
  13. Nataraj, Paluri S. V.; Barve, Jayesh J.: Reliable computation of frequency response plots for nonrational transfer functions to prescribed accuracy (2003)
  14. Neumaier, Arnold: Enclosing clusters of zeros of polynomials (2003)
  15. Rump, Siegfried M.: Ten methods to bound multiple roots of polynomials (2003)
  16. Rump, Siegfried M.; Zemke, Jens-Peter M.: On eigenvector bounds (2003)
  17. Ryoo, Cheon Seoung: Solving obstacle problems with guaranteed accuracy. (2003)
  18. Ryoo, Cheon Seoung; Nakao, Mitsuhiro T.: Numerical verification of solutions for obstacle problems. (2003)
  19. Yamamoto, Nobito; Hayakawa, Keisuke: Error estimation with guaranteed accuracy of finite element method in nonconvex polygonal domains. (2003)
  20. Zemke, Jens-Peter Max: Krylov subspace methods in finite precision: A unified approach (2003)

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