S.M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation I: Faithful Rounding.
SIAM Journal on Scientific Computing (SISC), 31(1): 189–224, 2008.
S. M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation II: Sign, K-fold Faithful and Rounding to Nearest.
SIAM Journal on Scientific Computing (SISC), 31(2):1269–1302, 2008.
S. M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM Journal of Matrix Analysis and Applications (SIMAX), 33(1):130–148, 2012.
S. M. Rump: Improved componentwise verified error bounds for least squares problems and underdetermined linear systems, Numerical Algorithms, 66:309–322, 2013.
R. Krawzcyk, A. Neumaier: Interval slopes for rational functions and associated centered forms,
SIAM Journal on Numerical Analysis 22, 604–616 (1985)
S. M. Rump: Expansion and Estimation of the Range of Nonlinear Functions,
Mathematics of Computation 65(216), pp. 1503–1512, 1996.
^S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.
^Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.
^L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.
^S.M. Rump. Verified sharp bounds for the real gamma function over the entire floating-point range. Nonlinear Theory and Its Applications (NOLTA), IEICE, Vol.E5-N, No. 3, July, 2014.
S.M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation I: Faithful Rounding.
SIAM Journal on Scientific Computing (SISC), 31(1): 189–224, 2008.
S. M. Rump, T. Ogita, and S. Oishi: Accurate Floating-point Summation II: Sign, K-fold Faithful and Rounding to Nearest.
SIAM Journal on Scientific Computing (SISC), 31(2):1269–1302, 2008.
S. M. Rump. Verified Bounds for Least Squares Problems and Underdetermined Linear Systems. SIAM Journal of Matrix Analysis and Applications (SIMAX), 33(1):130–148, 2012.
S. M. Rump: Improved componentwise verified error bounds for least squares problems and underdetermined linear systems, Numerical Algorithms, 66:309–322, 2013.
R. Krawzcyk, A. Neumaier: Interval slopes for rational functions and associated centered forms,
SIAM Journal on Numerical Analysis 22, 604–616 (1985)
S. M. Rump: Expansion and Estimation of the Range of Nonlinear Functions,
Mathematics of Computation 65(216), pp. 1503–1512, 1996.
^S.M. Rump, M. Kashiwagi: Implementation and improvements of affine arithmetic, Nonlinear Theory and Its Applications (NOLTA), IEICE, 2015.
^Lohner, R. J. (1987). Enclosing the solutions of ordinary initial and boundary value problems. Computer arithmetic, 225–286.
^L.B. Rall: Automatic Differentiation: Techniques and Applications, Lecture Notes in Computer Science 120, Springer, 1981.
^S.M. Rump. Verified sharp bounds for the real gamma function over the entire floating-point range. Nonlinear Theory and Its Applications (NOLTA), IEICE, Vol.E5-N, No. 3, July, 2014.