Sturm Sequence

Some articles on sturm, sequence, sturm sequence:

Sturm's Theorem
... In mathematics, the Sturm's sequence of a polynomial p is a sequence of polynomials associated to p and its derivative by a variant of Euclid's algorithm for polynomials ... Sturm's theorem expresses the number of distinct real roots of p located in an interval in terms of the number of changes of signs of the values of the Sturm's sequence ... the overall number of complex roots, counted with multiplicity, Sturm's theorem yields the number of distinct real roots and locates them in intervals ...
Greatest Common Divisor Of Two Polynomials - Univariate Polynomials With Coefficients in A Field - GCD and Root Finding - Sturm Sequence
... The Sturm sequence of a polynomial with real coefficients is the sequence of the remainders provided by a variant of Euclid's algorithm applied to the polynomial and ... For getting the Sturm sequence, one simply replaces the instruction of Euclid's algorithm by Let V(a) be the number of changes of signs in the sequence, when evaluated at a point a ... Sturm's theorem asserts that V(a)-V(b) is the number of real roots of the polynomial in the interval ...

Famous quotes containing the word sequence:

    We have defined a story as a narrative of events arranged in their time-sequence. A plot is also a narrative of events, the emphasis falling on causality. “The king died and then the queen died” is a story. “The king died, and then the queen died of grief” is a plot. The time sequence is preserved, but the sense of causality overshadows it.
    —E.M. (Edward Morgan)