Scientific Computing Seminar

Date:
Friday, August 27, 2004
Time:
1:00pm-2:00pm
Location:
50A-5132
Seminar Speaker:
Alan J. Laub
Department of Computer Science
UC Davis
Title:
Statistical Condition Estimation
Abstract:
Understanding the condition (or sensitivity) of problems solved with algorithms implemented in floating-point arithmetic is an essential step in assessing the accuracy of computed solutions. Standard approaches to measuring the condition of various problems in numerical linear algebra, for example, compress all sensitivity information into a single condition number. Thus, a loss of information can occur in situations in which this standard condition number does not accurately reflect the actual sensitivity in a solution or in particular entries of a solution. A method is described that overcomes these and other common deficiencies. The new procedure measures the effects on the solution of small random changes in the input data and, by properly scaling the results, obtains condition estimates for each component of a computed solution. This approach, which is referred to as small-sample statistical condition estimation (SCE), applies to both linear and nonlinear problems. In the former case, when an explicit Fréchet derivative is often available for the computed quantity in question, the method is especially efficient, costing no more than standard normwise or componentwise estimates. Moreover, SCE has the advantage of considerable flexibility. For example, it easily accommodates restrictions on, or structure associated with, allowable perturbations (symmetry, bandedness, etc.). The method has a rigorous statistical theory available for the probability of accuracy of the condition estimates. The theory of SCE is described along with several illustrative examples.
Sponsor of Seminar:
Esmond Ng
Scientific Computing

Contact Esmond G. Ng EGNg@lbl.gov