Inversion of extremely Ill-conditioned matrices in floating-point
Tóm tắt
Từ khóa
Tài liệu tham khảo
T. Dekker, A floating-point technique for extending the available precision. Numerische Mathematik,18 (1971), 224–242.
N. Higham, Accuracy and Stability of Numerical Algorithms, 2nd edition. SIAM Publications, Philadelphia, 2002.
ANSI/IEEE 754-2008: IEEE Standard for Floating-Point Arithmetic. New York, 2008.
D. Knuth, The Art of Computer Programming: Seminumerical Algorithms, Vol. 2. Addison Wesley, Reading, Massachusetts, 2004.
MATLAB User’s Guide, Version 7. The Math Works Inc., 2004.
T. Nishi, T. Ogita, S. Oishi and S. Rump, A method for the generation of a class of ill-conditioned matrices. 2008 International Symposium on Nonlinear Theory and Its Applications, NOLTA ’08, Budapest, Hungary, September 7–10, 2008, 53–56.
T. Ogita, S. Rump and S. Oishi, Accurate sum and dot product. SIAM Journal on Scientific Computing (SISC),26 (2005), 1955–1988.
T. Ohta, T. Ogita, S. Rump and S. Oishi, Numerical verification method for arbitrarily ill-conditioned linear systems. Transactions on the Japan Society for Industrial and Applied Mathematics (Trans. JSIAM),15 (2005), 269–287.
S. Oishi, K. Tanabe, T. Ogita and S. Rump, Convergence of Rump’s method for inverting arbitrarily ill-conditioned matrices. J. Comput. Appl. Math.,205 (2007), 533–544.
S. Rump, A class of arbitrarily ill-conditioned floating-point matrices. SIAM J. Matrix Anal. Appl. (SIMAX),12 (1991), 645–653.
S. Rump, INTLAB—INTerval LABoratory. Developments in Reliable Computing, T. Csendes (ed.), Kluwer Academic Publishers, Dordrecht, 1999, 77–104.
S. Rump, T. Ogita and S. Oishi, Accurate floating-point summation, part II: Sign,K-fold faithful and rounding to nearest. Accepted for publication in SISC, 2005–2008.
S. Rump, T. Ogita and S. Oishi, Accurate floating-point summation, part I: Faithful rounding. SIAM J. Sci. Comput.,31 (2008), 189–224.
N. Yamanaka, T. Ogita, S. Rump and S. Oishi, A parallel algorithm of accurate dot product. Accepted for publication, 2007.