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Explicit expressions for Sturm sequences

Published online by Cambridge University Press:  24 October 2008

H. J. Godwin
H. J. Godwin
Affiliation:
Department of Statistics and Computer Science, Royal Holloway and Bedford New Collge, Egham, Surrey TW20 0EX
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Extract

Sturm's theorem was announced in 1829 and various proofs were given soon after (see [2], p. 363 for details). It is given in various textbooks on algebra, e.g. in [1], pp. 448–453, where its application to finding the number and location of the real zeros of a polynomial is explained. It has been applied, in conjunction with Givens's method, to finding the eigenvalues of a matrix (see, e.g. [3], p. 494), and has been used recently in a neat computational form by Takeuchi [4] for investigating algebraic fields.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 100 , Issue 2 , September 1986 , pp. 225 - 227
Copyright
Copyright © Cambridge Philosophical Society 1986

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References

REFERENCES

[1] Barnard, S. and Child, J. M.. Higher Algebra (Macmillan, 1936).Google Scholar
[2] Cajori, F.. A History of Mathematics (Second edition) (Macmillan, 1919).Google Scholar
[3] Ralston, A.. A First Course in Numerical Analysis (McGraw-Hill, 1965).Google Scholar
[4] Takeuchi, K.. Totally real algebraic number fields of degree 5 and 6 with small discriminant. Saitama Mathematical Journal 2 (1984), 21–32.Google Scholar