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In order to find a root of a polynomial equation a_0x^n+a_1x^(n-1)+...+a_n=0, (1) consider the difference equation a_0y(t+n)+a_1y(t+n-1)+...+a_ny(t)=0, (2) which is known to ...

If x_0 is an ordinary point of the ordinary differential equation, expand y in a Taylor series about x_0. Commonly, the expansion point can be taken as x_0=0, resulting in ...

An algorithm for computing an Egyptian fraction.

A method for finding roots which defines P_j(x)=(P(x))/((x-x_1)...(x-x_j)), (1) so the derivative is (2) One step of Newton's method can then be written as ...

A generalization of the Bulirsch-Stoer algorithm for solving ordinary differential equations.

An algorithm for computing an Egyptian fraction (Stewart 1992).

An algorithm which isolates roots in the complex plane by generalizing one-dimensional bracketing.

An algorithm for computing an Egyptian fraction.

Marsaglia (1972) has given a simple method for selecting points with a uniform distribution on the surface of a 4-sphere. This is accomplished by picking two pairs of points ...

A factorization algorithm which works by expressing N as a quadratic form in two different ways. Then N=a^2+b^2=c^2+d^2, (1) so a^2-c^2=d^2-b^2 (2) (a-c)(a+c)=(d-b)(d+b). (3) ...