Self-validating methods.

• 4-04.171V
  

  S.M. Rump and J. Zemke. On eigenvector bounds.BIT, 43:823-837, 2004.

• 4-04.176V
  

  T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product with Applications. Proceedings of 2004 IEEE International Symposium on Computer Aided Control Systems Design, Taipei, pages 152-155, 2004.

• 4-04.179V
  

  S.M. Rump. Computer-Assisted Proofs I. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(3):214-223, 2004.

• 4-04.180V
  

  S.M. Rump. Computer-Assisted Proofs II. Bulletin of the Japan Society for Industrial and Applied Mathematics (Bull. JSIAM), 14(4):44-57, 2004. translated by T. Ogita.

• 4-04.182V
  

  S.M. Rump and T. Ogita. Super-Fast Validated Solution of Linear Systems. Journal of Computational and Applied Mathematics (JCAM), 199(2):199-206, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004).

• 4-04.184V
  

  S.M. Rump. High Precision Evaluation of Nonlinear Functions. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 733-736, 2005.

• 4-04.186V
  

  S.M. Rump. Computer-assisted proofs and Self-Validating Methods. In B. Einarsson, editor, Handbook on Acuracy and Reliability in Scientific Computation, pages 195-240. SIAM, 2005.

• 4-04.187V
  

  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. Componentwise Verified Solutions of Linear System Suited for Java. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 749-752, 2005.

• 4-04.188V
  

  K. Ozaki, T. Ogita, S. Miyajima, S. Oishi, and S.M. Rump. A Method of obtaining verified solutions for linear systems suited for Java. Journal of Computational and Applied Mathematics (JCAM), 199(2):337-344, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004).

• 4-04.189V
  

  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Verification Method for Arbitrarily Ill-conditioned Linear Systems. Trans. JSIAM, 15(3):269-287, 2005.

• 4-04.190V
  

  T. Ohta, T. Ogita, S.M. Rump, and S. Oishi. Numerical Method for Dense Linear Systems with Arbitrariliy Ill-conditioned Matrices. In Proceedings of 2005 International Symposium on Nonlinear Theory and its Applications, Bruge, Belgium, October 18-21, pages 745-748, 2005.

• 4-04.191V
  

  T. Ogita, S.M. Rump, and S. Oishi. Accurate Sum and Dot Product. SIAM Journal on Scientific Computing (SISC), 26(6):1955-1988, 2005.

• 4-04.195V
  

  C. Jansson, D. Chaykin, and C. Keil. Rigorous Error Bounds for the Optimal Value in Semidefinite Programming. SIAM Journal on Numerical Analysis (SINUM), 46(1) : 180-200, 2007.

• 4-04.198V
  

  C. Jansson. On Verifed Computation in Combinatorial Optimization. International Symposium on Nonlinear Theory and its Applications (NOLTA2005), Bruges, Belgium, pages 714-717, 2005.

• 4-04.204V
  

  S.M. Rump. Verification of Positive Definiteness. BIT Numerical Mathematics, 46:433-452, 2006.

• 4-04.206V
  

  S.M. Rump. Error bounds for extremely ill-conditioned problems. In Proceedings of 2006 International Symposium on Nonlinear Theory and its Applications, Bologna, Italy, September 11-14, 2006.

• 4-04.209V
  

  V. Kreinovich and S.M. Rump. Towards Optimal Use of Multi-Precision Arithmetic: A Remark. Reliable Computing, 12:365-369, 2006.

• 4-04.210V
  

  G. Alefeld, M.T. Nakao, and S.M. Rump. Preface. Journal of Computational and Applied Mathematics (JCAM), 199(2):197-198, 2006. Special issue on Scientific Computing, Computer Arithmetic, and Validated Numerics (SCAN 2004).

• 4-04.211V
  

  N. Yamanaka, T. Ogita, S.M. Rump, and S. Oishi. A Parallel Algorithm of Accurate Dot Product. accepted for publication. Parallel Computing, 34(6-8):392-410, 2008.

• 4-04.214V
  

   K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate Matrix Multiplication with Multiple Floating-point Numbers. In Proceedings of 2007 International Symposium on Nonlinear Theory and its Applications, Vancouver, Canada, September 16-19, 2007.

• 4-04.218V
  

   S. Oishi, K. Tanabe, T. Ogita, and S.M. Rump. Convergence of Rump's method for inverting arbitrarily ill-conditioned matrices. J. Comput. Appl. Math., 205(1):533-544, 2007.

• 4-04.219V
  

   K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Fast and robust algorithm for geometric predicates using floating-point arithmetic. Trans. JSIAM, 4(16):553-562, 2006. [in Japanese].

• 4-04.220V
  

   T. Ogita, S.M. Rump, and S. Oishi. Verified solution of linear systems without directed rounding. Technical Report 2005-04, Advanced Research Institute for Science and Engineering, Waseda University, Tokyo, Japan, 2005.

• 4-04.221V
  

  S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419-431, 2009.
  

• 4-04.222V
  

  S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM), 26:1-29, 2009.
  

• 4-04.223V
  

  S.M. Rump, T. Ogita, and S. Oishi. Fast high precision summation. Appears in Nonlinear Theory and Its Applications (NOLTA), IEICE, 2010.

• 4-04.224V
  

  S.M. Rump. Ultimately Fast Accurate Summation. accepted for publication, 2009.

• 4-04.225V
  

  T. Nishi, T. Ogita, S. Oishi, and S. M. Rump. A Method for the Generation of a Class of Ill-conditioned Matrices. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 53-56, 2008.

• 4-04.226V
  

  K. Ozaki, T. Ogita, S. M. Rump, and S. Oishi. Accurate matrix multiplication by using level 3 BLAS operation. In Proceedings of the 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, pages 508-511. IEICE, 2008.

• 4-04.227V
  

  S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. In 2008 International Symposium on Nonlinear Theory and its Applications, NOLTA'08, Budapest, Hungary, September 7-10, pages 516-519, 2008.

• 4-04.229V
  

  C. Keil. Verified Linear Programming - a Comparison. submitted for publication, 2008.

• 4-04.230V
  

  C. Jansson. A classical interpretation of quantum mechanics and the measurement problem. quant-ph, 2008.

• 4-04.231V
  

  S.M. Rump, P. Zimmermann, S. Boldo, and G. Melquiond. Computing predecessor and successor in rounding to nearest. BIT Numerical Mathematics, 49(2):419-431, 2009.

• 4-04.232V
  

  S.M. Rump and H. Sekigawa. The ratio between the Toeplitz and the unstructured condition number. Operator Theory: Advances and Applications, 199:397-419, 2009.

• 4-04.233V
  

  S. M. Rump and S. Oishi. Verified Error Bounds for Double Roots of Nonlinear Equations. In 2009 International Symposium on Nonlinear Theory and its Applications, NOLTA'09, Sapporo, Japan, 2009.

• 4-04.234V
  

  S.M. Rump and S. Graillat. Verified error bounds for multiple roots of systems of nonlinear equations. Numerical Algorithms, 54(3):359-377, 2009. DOI 10.1007/s11075-009-9339-3.

• 4-04.235V
  

  S.M. Rump. Ultimately Fast Accurate Summation. SIAM Journal on Scientific Computing (SISC), 31(5):3466-3502, 2009.

• 4-04.236V
  

  S.M. Rump. Inversion of extremely ill-conditioned matrices in floating-point. Japan J. Indust. Appl. Math. (JJIAM),  26:249-277, 2009.

• 4-04.237V
  

  S.M. Rump. Error-Free Transformations and ill-conditioned problems. In Proceedings of the "International workshop on verified computations and related topics", University of Karlsruhe, March 7-10, 2009.

• 4-04.238V
  

  K. Ozaki, T. Ogita, S.M. Rump, and S. Oishi. Adaptive and Efficient Algorithm for 2D Orientation Problem. Japan J. Indust. Apl. Math., 26:215-231, 2009.

• 4-04.239V
  

  S. Oishi, T. Ogita, and S. M. Rump. Iterative Refinement for Ill-conditioned Linear Equations. Japan J. Indust. Appl. Math., 26(2):465-476, 2009.

• 4-04.240V
  

  S. Miyajima, T. Ogita, S.M. Rump, and S. Oishi. Fast Verification ofr All Eigenpairs in Symmetric Positive Definite Generalized Eigenvalue Problem. accepted for publication in Reliable Computing, 2009.

• 4-04.243V
  

  C. Jansson. On Verified Numerical Computations in Convex Programming. Japan J. Indust. Appl. Math., 26:337-363, 2009.

• 4-04.244V
  

  F. Bünger. Minimizing and maximizing the Euclidean norm of the product of two polynomials. Advances in Computational Mathematics 35(2):193-215, 2011.

• 4-04.245V
  

  F. Bünger. Verified solutions of two-point boundary problems for nonlinear oscillators, special issue on Recent Progress in Verified Numerical Computations of the journal Nonlinear Theory and Its Applications, Nonlinear Theory and its Applications (NOLTA), IEICE, volume E94-N, no. 1, 2011.

• 4-04.248V
  

  B. Kearfott, M. Nakao, S. Neumaier, A. Rump. S.P. Shary, and P. Van Hentenryck. Standardized notation in interval analysis. Reliable Computing, 15(1):7-13, 2010.
  

• 4-04.249V
  

  S.M. Rump. A Model Problem for Global Optimization.In Nonlinear Theory and Its Appilcations (NOLTA), volume 1, pages 1-6. IEICE, 2010.

• 4-04.250V
  

  S.M. Rump. Accurate and Reliable Computing in Floating-Point Arithmetic. In K. Fukuda et al., editor,Proceedings of the Third International Congress on Mathematical Software, Kobe, Japan, September 13-17, 2010 (ICMS 2010), volume 6327 ofLecture Notes in Computer Science (LNCS), pages 105-108, 2010.

• 4-04.251V
  

  S.M. Rump. Verification methods: Rigorous results using floating-point arithmetic. Acta Numerica, 19:287-449, 2010.

• 4-04.252V
  

  S.M. Rump and S. Oishi. Verified computation of a disc containing exactly k roots of a univariate nonlinear function.Nonlinear Theory and Its Applications (NOLTA), E93-N(Vol. (10)), 2010.

• 4-04.253V
  

  S.M. Rump, T. Ogita, and S. Oishi. Fast high precision summation. Appears in Nonlinear Theory and Its Applications (NOLTA), IEICE, 2010.