Numerical Efficiency Profile Functions 1)

Certain Incomplete Numerical Functions*

Numerical Evaluation of Special Functions

Higher transcendental functions continue to play varied and important roles in investigations by engineers, mathematicians, scientists and statisticians. The purpose of this paper is to assist in locating useful approximations and software for the numerical generation of these functions, and to offer some suggestions for future developments in this field. March 1994 December 200

Numerical Hilbert functions for Macaulay2

The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure. These techniques are numerically stable, and can be used with floating point arithmetic over the complex numbers. They provide a viable alternative in this setting to purely symbolic methods such as standard bases. ...

Numerical Analysis: Approximation of Functions

Task: A polynomial can be factorized to the product of linear polynomials, but only for orders up to 4. Numerical solution is possible, but it is imprecise and division leaves a remainder. Also this is a subject of numerical anaysis. Task: Linear algebra: “A system of linear equations Ax = b has a unique solution x = A−1b if and only if det A 6= 0.” Programming: “Real numbers cannot be tested f...

Numerical Computation of Matrix Functions

8