The algebraic eigenvalue problem
The algebraic eigenvalue problem
Error Analysis of Direct Methods of Matrix Inversion
Journal of the ACM (JACM)
Rounding Errors in Algebraic Processes
Rounding Errors in Algebraic Processes
ACM Transactions on Mathematical Software (TOMS)
A Survey of Indexing Techniques for Sparse Matrices
ACM Computing Surveys (CSUR)
A note on estimating the error in Gaussian elimination without pivoting
ACM SIGNUM Newsletter
A proposed numerical accuracy control system
Symposium on Interactive Systems for Experimental Applied Mathematics: Proceedings of the Association for Computing Machinery Inc. Symposium
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An error analysis of direct methods (i.e., Gaussian elimination or triangular factorization) of solving simultaneous linear algebraic equations is performed in the backward mode, in which the computational errors are expressed as perturbations on the data. Bounds are found for perturbations on the coefficients of the equations, leaving the right-hand sides unchanged. These bounds can be evaluated concurrently with the computation itself, with only a small increase in computing effort. Because they use information obtained during the solution process, these bounds avoid exaggerating the magnitude of the error, and so are also useful as error estimates.