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XIX.—On the Reciprocation of Certain Matrices

Published online by Cambridge University Press:  15 September 2014

A. R. Collar
A. R. Collar
Affiliation:
Aerodynamics Department, the National Physical Laboratory.*
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Extract

In a recent paper (Frazer, Jones, and Skan, 1937) some methods are discussed for the approximate representation of functions by means of polynomials. The coefficients in the polynomials are determined by the equation

where c is the column of coefficients, h is a column of known constants, and M is a matrix which depends on the method of representation adopted. The present paper shows how the reciprocal matrix M-1 can be computed rapidly and simply in the two cases where M is a moment matrix or an alternant matrix.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 59 , 1940 , pp. 195 - 206
Copyright
Copyright © Royal Society of Edinburgh 1940

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References

References to Literature

Aitken, A. C., 1933. “On the Graduation of Data by the Orthogonal Polynomials of Least Squares,” Proc. Roy. Soc. Edin., vol. liii, pp. 54–78.Google Scholar
Courant, R., and Hilbert, D., 1924. Methoden der Mathematischen Physik (Berlin), chap. ii.CrossRefGoogle Scholar
Frazer, R. A., Duncan, W. J., and Collar, A. R., 1938. Elementary Matrices (Cambridge), chap. iv.CrossRefGoogle Scholar
Frazer, R. A., Jones, W. P., and Skan, S. W., 1937. “Approximations to Functions and to the Solutions of Differential Equations,” Reports and Memoranda of the Aeronautical Research Committee, No. 1799.Google Scholar