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On a Simple Method for Solving Simultaneous Linear Equations by a Successive Approximation Process

Published online by Cambridge University Press:  28 July 2016

J. Morris
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Extract

Simultaneous equations of three or more variables are notoriously trouble some to solve numerically and, moreover, are frequently sensitive for certain relative values of the variables. This usually precludes the use of the slide rule and in consequence resort has to be had to accurate working to an increasing number of decimal places involving much labour even with a calculating machine.

A method is here given which is applicable to certain classes of equations of frequent occurrence in mathematical physics and engineering science, which method is a combination of what is knovwi as the Iteration process and the means of applying this principle to end moment distribution devised by Professor Hardy Cross.

Type
Research Article
Information
The Aeronautical Journal , Volume 39 , Issue 292 , April 1935 , pp. 349 - 351
Copyright
Copyright © Royal Aeronautical Society 1935

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References

Note on page 349 * Analysis of Continuous Frames by Distributing Fixed End Moments. H. Cross,' Amer. Soc. of C.E., May, 1980.

Note on page 351 * On further invesligalion it appears that the condition for convergency of the process for this example is that the following equation in A (which is of general form), viz.,

must have its real roots numerically less than unity and, in the case of imaginary roots, the moduli must be leas than unity. Similarly for the general case of n variables.