Efficient and Numerically Stable Computations

Mark Sofroniou
Wolfram Research, Inc.

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Mark Sofroniou

Topics covered will include the stability of various forms of symbolic expressions and some examples of how to make transformations to improve stability/performance. A new package for common subexpression elimination will be shown, and examples will be given to illustrate how to use it in conjunction with the compiler and with packed arrays. Significance arithmetic is described, including the linear error-accumulation model and some examples of how this works to highlight flaws in the use of fixed-precision arithmetic.