Computational Accuracy of Linear Stationary Iterations.
HAWAII UNIV HONOLULU
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In the report the author analyzed floating-point round-off errors in iterative processes. A conditional probabilistic model of the round-off errors was derived. This probabilistic model shows that the round-off errors depend only on the computed result. Using this computational model and the probabilistic error model, one is able to bound the covariance matrix of the accumulated round-off error from above and below by a sequence of positive semidefinite matrices. This covariance matrix is a sum of positive semidefinite matrices with each matrix corresponding to a set of the round-off errors. From this one is able to interpret the computed iterate as a signal plus an orthogonal noise component. Author
- Statistics and Probability
- Computer Programming and Software