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Newton's method for finding roots of a complex polynomial f entails iterating the function z-[f(z)/f^'(z)], which can be viewed as applying the Euler backward method with ...

The Remez algorithm (Remez 1934), also called the Remez exchange algorithm, is an application of the Chebyshev alternation theorem that constructs the polynomial of best ...

Adams' method is a numerical method for solving linear first-order ordinary differential equations of the form (dy)/(dx)=f(x,y). (1) Let h=x_(n+1)-x_n (2) be the step ...

The consideration of the result of a numerical calculation as a function of an adjustable parameter (usually the step size). The function can then be fitted and evaluated at ...

A genetic algorithm is a class of adaptive stochastic optimization algorithms involving search and optimization. Genetic algorithms were first used by Holland (1975). The ...

The conjecture that Frey's elliptic curve was not modular. The conjecture was quickly proved by Ribet (Ribet's theorem) in 1986, and was an important step in the proof of ...

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 ...

Values one step outside the hinges are called inner fences, and values two steps outside the hinges are called outer fences. Tukey calls values outside the outer fences far ...

A proof or demonstration is said to be rigorous if the validity of each step and the connections between the steps is explicitly made clear in such a way that the result ...

The difference X_1-X_2 of two uniform variates on the interval [0,1] can be found as P_(X_1-X_2)(u) = int_0^1int_0^1delta((x-y)-u)dxdy (1) = 1-u+2uH(-u), (2) where delta(x) ...