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An initial point that provides safe convergence of Newton's method (Smale 1981; Petković et al. 1997, p. 1).

A procedure for finding the quadratic factors for the complex conjugate roots of a polynomial P(x) with real coefficients. (1) Now write the original polynomial as ...

The apodization function A(x)=(1-(x^2)/(a^2))^2. Its full width at half maximum is sqrt(4-2sqrt(2))a. Its instrument function is ...

The apodization function A(x)=cos((pix)/(2a)). Its full width at half maximum is 4a/3. Its instrument function is I(k)=(4acos(2piak))/(pi(1-16a^2k^2)), which has a maximum of ...

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

An algorithm for finding roots for quartic equations with complex roots.

Let P=a_1x+a_2x^2+... be an almost unit in the integral domain of formal power series (with a_1!=0) and define P^k=sum_(n=k)^inftya_n^((k))x^n (1) for k=+/-1, +/-2, .... If ...

For p(z)=a_nz^n+a_(n-1)z^(n-1)+...+a_0, (1) polynomial of degree n>=1, the Schur transform is defined by the (n-1)-degree polynomial Tp(z) = a^__0p(z)-a_np^*(z) (2) = ...

The number of real roots of an algebraic equation with real coefficients whose real roots are simple over an interval, the endpoints of which are not roots, is equal to the ...

Augmentation is the dual operation of truncation which replaces the faces of a polyhedron with pyramids of height h (where h may be positive, zero, or negative) having the ...