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Analog Computer for the Roots of Algebraic Equations

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1 Author(s)
Lofgren, L. ; Research engineer, Swedish Research Institute of National Defense, Stockholm, Sweden

An electronic analog machine for computing the roots of algebraic equations of degrees through the eighth is described. The coefficients of the equation may be complex. The roots are indicated as points in the complex number plane light points on the screen of a cathode-ray tube. Once per second the roots are displayed, and when some of the coefficients are varied the corresponding curves described by the roots are made visible by the persistence of light emission from the screen. An accurate determination of the roots is obtained by means of a comparison-root which can be moved all over the number plane and thus be brought to coincide with a root. The comparison-root is displayed by a scanning system, which also controls the positions of the roots, and so it is possible to obtain an accurate reading not influenced by distortion in the cathode-ray tube. By means of a normalizing device, the voltage level in the machine is kept high throughout the computation, and so all the roots are determined with about the same percental accuracy. The modulus of an error will normally be of the magnitude of 1 per cent of the corresponding root-modulus.

Published in:

Proceedings of the IRE  (Volume:41 ,  Issue: 7 )