Computational Accuracy of Linear Stationary Iterations.
Abstract
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 1971
- Accession Number
- AD0737116
Entities
People
- Richard H. Yamamoto
Organizations
- University of Hawaiʻi System