Computational errors in closed‐form expressions with an electromagnetic example: The conducting‐sphere response

Author:

Brown R. James1

Affiliation:

1. Department of Geology and Geophysics, University of Calgary, Calgary, Alta., Canada T2N 1N4

Abstract

Errors are expected to result from the numerical evaluation of approximate mathematical expressions such as truncated series and finite‐element solutions, from exact expressions based on approximate theory (e.g., perfect gas law), or from analysis based on field data. Many theoretical problems in science—and geophysics is no exception—involve a wholly correct mathematical expression that is beset with computational difficulties arising solely from numerical calculations using the expression. For example, even with modern computers, computation from a slowly convergent series expression can demand an amount of computation time for convergence that is impractically great. Recurrence formulas themselves sometimes propagate errors, often in a nonlinear manner; Acton (1970) provides further insight into this and other aspects of numerical methods generally. Another potential trouble area is the application of slowly convergent iterative matrix methods to least‐squares problems. (Olson, 1987). For such cases, numerical difficulty should be expected.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

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