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Patrick Fitzpatrick, "Extending Backward Error Assertions to Tolerance of Large Errors in Floating Point Computations," IEEE Transactions on Computers, vol. 46, no. 4, pp. 505510, April, 1997.  
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@article{ 10.1109/12.588072, author = {Patrick Fitzpatrick}, title = {Extending Backward Error Assertions to Tolerance of Large Errors in Floating Point Computations}, journal ={IEEE Transactions on Computers}, volume = {46}, number = {4}, issn = {00189340}, year = {1997}, pages = {505510}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.588072}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Extending Backward Error Assertions to Tolerance of Large Errors in Floating Point Computations IS  4 SN  00189340 SP505 EP510 EPD  505510 A1  Patrick Fitzpatrick, PY  1997 KW  Fault tolerance KW  algorithmbased fault tolerance KW  backward error assertions KW  floating point computation. VL  46 JA  IEEE Transactions on Computers ER   
Abstract—The use of backward error assertions combined with iterative refinement has been suggested for the correction of small fault induced errors in the floating point solution of linear systems. We extend this to the correction of large errors, typically caused by the failure of a single processor (or column of processors) in an array.
[1] C. Anfinson and F.T. Luk, "A Linear Algebraic Model of AlgorithmBased Fault Tolerance," IEEE Trans. Computers, Dec. 1988, pp. 15991604.
[2] D.L. Boley,G.H. Golub,S. Makar,N. Saxena, and E.J. McCluskey,"Floating Point Fault Tolerance Using Backward Error Assertions," IEEE Trans. Computers, Special Issue on FaultTolerant Computing, vol. 44, no. 2, pp. 302311, Feb. 1995.
[3] R.P. Brent, F.T. Luk, and C.J. Anfinson, "Checksum Schemes for Fault Tolerant Systolic Computing," Mathematics in Signal Processing II, J.G. McWhirter, ed., pp. 791804.Oxford: Oxford Univ. Press, 1990.
[4] M.P. Connolly and P. Fitzpatrick, "Fault Tolerant QR Decomposition for Adaptive Signal Processing," SPIE: Advanced Signal Processing, vol. 2,296, pp. 740750, 1994.
[5] M.P. Connolly and P. Fitzpatrick, "Fault Tolerant QRD Recursive Least Squares," IEE Proc.E Computers and Digital Techniques, 143, pp. 137144, 1996.
[6] P. Fitzpatrick, "A Coding Theoretic Approach to Fault Tolerant Matrix Decompositions and Solution of Linear Systems of Equations," Mathematics in Signal Processing III, J.G. McWhirter, ed., pp. 4150.Oxford: Clarendon Press, 1994.
[7] P. Fitzpatrick, "On Fault Tolerant Matrix Decomposition," J. VLSI Signal Processing, vol. 8, pp. 293303, 1994.
[8] P. Fitzpatrick, "Fault Tolerant Linear Algebra," Bull. Inst. Math. and Its Applicationss., vol. 32, pp. 1722, 1996.
[9] P. Fitzpatrick and C.C. Murphy, "Fault Tolerant Matrix Triangularization and Solution of Linear Systems of Equations," Proc. Application Specific Array Processors, pp. 469480. IEEE CS Press, 1992.
[10] P. Fitzpatrick and C.C. Murphy, "Solution of Linear Systems of Equations in the Presence of two Transient Errors," IEE Proc.E, vol. 140, pp. 247254, 1993.
[11] G.H. Golub and C.F. Van Loan, Matrix Computations, second edition. Johns Hopkins Univ. Press, 1989.
[12] K.H. Huang and J.A. Abraham, "AlgorithmBased Fault Tolerance for Matrix Operations," IEEE Trans. Computers, vol. 33, pp. 518528, 1984.
[13] N.J. Higham, "Iterative Refinement Enhances the Stability of QR Factorization Methods for Solving Liner Equations," BIT, vol. 31, pp. 447468, 1991.
[14] JY. Jou and J.A. Abraham, "FaultTolerant Matrix Arithmetic and Signal Processing on Highly Concurrent Computing Structures," Proc. IEEE, vol. 74, pp. 732741, 1986.
[15] M. Jankowski and H. Wozniakowski, "Iterative Refinement Implies Numerical Stability," BIT, vol. 17, pp. 303311, 1977.
[16] F.T. Luk and H. Park, “A Fault Tolerance Matrix Triangularizations on Systolic Arrays,” IEEE Trans. Computers, vol. 37, no. 11, pp. 14341438, Nov. 1988.
[17] F.T. Luk and H. Park, “An Analysis of AlgorithmBased Fault Tolerance Techniques,” J. Parallel and Distributed Computing, vol. 5, pp. 172184, 1988.
[18] H. Park, "On Multiple Error Correction in Matrix Triangularizations Using Checksum Schemes," J. Parallel and Distributed Computing, vol. 14, pp. 9097, 1992.
[19] A. RoyChowdhury and P. Banerjee, "AlgorithmBased Fault Location and Recovery for Matrix Computations," Proc. 24th FTCS, pp. 3848, 1994.
[20] A. RoyChowdhury and P. Banerjee,"A New Error Analysis Based Method for Tolerance Computation for AlgorithmBased Checks," IEEE Trans. Computers, vol. 45, no. 2, pp. 238243, Feb. 1996.
[21] R.D. Skeel, "Iterative Refinement Implies Numerical Stability for Gaussian Elimination," Math. Comp. vol. 35, pp. 817832