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J.W. Demmel, Xiaoye Li, "Faster Numerical Algorithms Via Exception Handling," IEEE Transactions on Computers, vol. 43, no. 8, pp. 983992, August, 1994.  
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@article{ 10.1109/12.295860, author = {J.W. Demmel and Xiaoye Li}, title = {Faster Numerical Algorithms Via Exception Handling}, journal ={IEEE Transactions on Computers}, volume = {43}, number = {8}, issn = {00189340}, year = {1994}, pages = {983992}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.295860}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Faster Numerical Algorithms Via Exception Handling IS  8 SN  00189340 SP983 EP992 EPD  983992 A1  J.W. Demmel, A1  Xiaoye Li, PY  1994 KW  linear algebra; parallel algorithms; digital arithmetic; exception handling; convergence of numerical methods; eigenvalues and eigenfunctions; exception handling; fast numerical algorithms; parallel machines; unstable algorithms; numerical linear algebra; LAPACK library; IEEE floating point arithmetic. VL  43 JA  IEEE Transactions on Computers ER   
An attractive paradigm for building fast numerical algorithms is the following: 1) try a fast but occasionally unstable algorithm, 2) test the accuracy of the computed answer, and 3) recompute the answer slowly and accurately in the unlikely event it is necessary. This is especially attractive on parallel machines where the fastest algorithms may be less stable than the best serial algorithms. Since unstable algorithms can overflow or cause other exceptions, exception handling is needed to implement this paradigm safely. To implement it efficiently, exception handling cannot be too slow. We illustrate this paradigm with numerical linear algebra algorithms from the LAPACK library.
[1] E. Anderson, "Robust triangular solves for use in condition estimation," Comput. Sci. Dep. Tech. Rep. CS91142, Univ. of Tennessee, Knoxville, 1991. (LAPACK Working Note #36).
[2] N. H. Madhavji, "The Prism model of changes," inProc. 13th Int. Conf. on Software Eng. Los Alamitos, CA: IEEE Computer Soc. Press, 1991, pp. 166177.
[3] ANSI/IEEE, New York,IEEE Standard for Binary Floating Point Arithmetic, Std 7541985 ed., 1985.
[4] ANSI/IEEE, New York.IEEE Standard for Raix Independent Floating Point Arithmetic, Std 8541987 ed., 1987.
[5] J. Demmel, "Underflow and the reliability of numerical software,"SIAM J. Sci. Statist. Comput., vol. 5, no. 4, pp. 887919, Dec. 1984.
[6] J. Demmel, "Specifications for robust parallel prefix operations,"Technical Report, Thinking Machines Corp., 1992.
[7] J. Demmel and X. Li, "Faster numerical algorithms via exception handling," inProc. 11th Symp. Comput. Arithmetic, M. J. Irwin, E. Swartzlander, and G. Jullien, Eds., Windsor, ON, Canada, June 29July 2 1993. IEEE Computer Society Press, available as all.ps.Z via anonymous ftp from trftp.cs.berkeley.edu, in directory pub/techreports/cs/csd93728; software is csd93728.shar.Z.
[8] I. S. Dhillon and J. W. Demmel, "A parallel algorithm for the symmetric tridiagonal eigenproblem and its implementation on the CM5," in progress, 1993.
[9] J.J. Dongarra et al., "A Set of Level 3 Basic Linear Algebra Subprograms,"ACM Trans. Math. Software, Vol. 16, No. 1, 1990, pp. 117.
[10] J. Dongarra et al., "An Extended Set of Fortran Basic Linear Algebra Subroutines,"ACM Trans. Math. Software, Vol. 14, No. 1, Mar. 1988, pp. 117.
[11] R. L. Sites, Ed.,Alpha Architecture Reference Manual. Burlington, MA: Digital Press, 1992.
[12] G. H. Golub and C. F. Van Loan,Matrix Computations, 2nd ed. Baltimore, MD: Johns Hopkins Press, 1989.
[13] W. W. Hager, "Condition estimators,"SIAM J. Sci. Statist. Comput., vol. 5, pp. 311316, 1984.
[14] N. J. Higham, "Algorithm 674: FORTRAN codes for estimating the onenorm of a real or complex matrix, with applications to condition estimation,"ACM Trans. Math. Software, vol. 14, pp. 381396, 1988.
[15] The Spare Architecture Manual, Version 8, Part 800139912, Sun Microsystems, Inc., Mountain View, Calif., Dec. 1990.
[16] W. Kahan, "Accurate eigenvalues of symmetric tridiagonal matrix," Computer Sci. Dep., Tech. Rep. CS41, Stanford Univ., Stanford, CA, July 1966 (revised June 1968).
[17] G. Kane,MIPS RISC Architecture, PrenticeHall, Englewood Cliffs, N.J., 1988.
[18] C. Lawson et al., "Basic Linear Algebra Subprograms for Fortran Usage,"ACM Trans. Math. Software, Vol. 5, No. 3, Sept. 1979, pp. 308323.
[19] Thinking Machines Corporation,The Connection Machine CM5 Technical Summary, Cambridge MA, Oct. 1991.