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Explicit expressions for Sturm sequences

Published online by Cambridge University Press:  24 October 2008

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

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
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), 2132.Google Scholar