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Technically, a point z 0 is a pole of a function f if it is a zero of the function 1/f and 1/f is holomorphic (i.e. complex differentiable) in some neighbourhood of z 0. A function f is meromorphic in an open set U if for every point z of U there is a neighborhood of z in which at least one of f and 1/f is holomorphic.
In mathematics, the Milne-Thomson method is a method for finding a holomorphic function whose real or imaginary part is given. [1] It is named after Louis Melville Milne-Thomson . Introduction
One important consequence of the theorem is that path integrals of holomorphic functions on simply connected domains can be computed in a manner familiar from the fundamental theorem of calculus: let be a simply connected open subset of , let : be a holomorphic function, and let be a piecewise continuously differentiable path in with start ...
In computational complexity theory, Karp's 21 NP-complete problems are a set of computational problems which are NP-complete.In his 1972 paper, "Reducibility Among Combinatorial Problems", [1] Richard Karp used Stephen Cook's 1971 theorem that the boolean satisfiability problem is NP-complete [2] (also called the Cook-Levin theorem) to show that there is a polynomial time many-one reduction ...
As stated above, the complexity of finding a convex hull as a function of the input size n is lower bounded by Ω(n log n). However, the complexity of some convex hull algorithms can be characterized in terms of both input size n and the output size h (the number of points in the hull). Such algorithms are called output-sensitive algorithms.
The following is an example of a possible implementation of Newton's method in the Python (version 3.x) programming language for finding a root of a function f which has derivative f_prime. The initial guess will be x 0 = 1 and the function will be f ( x ) = x 2 − 2 so that f ′ ( x ) = 2 x .
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In numerical analysis, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function f is a number x such that f ( x ) = 0 . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form , root-finding algorithms provide approximations to zeros.