Fast Inclusion of Interval Matrix Multiplication

Alefeld, G. and Herzberger, J.: Introduction to Interval Computations, Academic Press, New York, 1983.

Dongarra, J. J., Croz, J. D., Duff, I. S., and Hammarling, S.: Algorithm 679: A Set of Level 3 Basic Linear Algebra Subprograms, ACMTrans. Math. Softw. 16 (1990), pp. 1–17.

Golub, G. H. and Van Loan, C. F.: Matrix Computations, 3rd ed., The Johns Hopkins University Press, Baltimore and London, 1996.

Kulisch, U. W. and Miranker, W. L.: The Arithmetic of the Digital Computer: A New Approach, SIAM Review 28 (1986), pp. 1–40.

Oishi, S.: Fast Enclosure of Matrix Eigenvalues and Singular Values via Rounding Mode Controlled Computation, Linear Alg. Appl. 324 (2001), pp. 133–146.

Oishi, S. and Rump, S. M.: Fast Verification of Solutions of Matrix Equations, Numer. Math. 90 (4)(2002), pp. 755–773.

Rump, S. M.: Computational Error Bounds for Multiple or Nearly Multiple Eigenvalues, Linear Alg. Appl. 324 (2001), pp. 209–226.

Rump, S. M.: Fast and Parallel Interval Arithmetic, BIT 39 (3)(1999), pp. 534–554.

Rump, S. M.: INTLAB—INTerval LABoratory, Version 4.1.1, 2003, http://www.ti3.tu-harburg.de/~rump/intlab/

Rump, S. M.: On the Solution of Interval Linear Systems, Computing 47 (1992), pp. 337–353.

Whaley, R. C., Petitet, A., and Dongarra, J. J.: Automated Empirical Optimization of Software and the ATLAS Project, Parallel Comput. 27 (1–2)(2001), pp. 3–25.