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Horner's method evaluates a polynomial using repeated bracketing: + + + + + = + (+ (+ (+ + (+)))). This method reduces the number of multiplications and additions to just Horner's method is so common that a computer instruction "multiply–accumulate operation" has been added to many computer processors, which allow doing the addition and multiplication operations in one combined step.
An evaluation function, also known as a heuristic evaluation function or static evaluation function, is a function used by game-playing computer programs to estimate the value or goodness of a position (usually at a leaf or terminal node) in a game tree. [1]
Gauss–Legendre quadrature is optimal in a very narrow sense for computing integrals of a function f over [−1, 1], since no other quadrature rule integrates all degree 2n − 1 polynomials exactly when using n sample points. However, this measure of accuracy is not generally a very useful one---polynomials are very simple to integrate and ...
In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. [1] It is also known as Rosenbrock's valley or Rosenbrock's banana function. The global minimum is inside a long, narrow, parabolic-shaped flat ...
This approach requires the function evaluations to grow exponentially as the number of dimensions increases. Three methods are known to overcome this so-called curse of dimensionality. A great many additional techniques for forming multidimensional cubature integration rules for a variety of weighting functions are given in the monograph by ...
A B-spline function is a combination of flexible bands that is controlled by a number of points that are called control points, creating smooth curves. These functions are used to create and manage complex shapes and surfaces using a number of points. B-spline function and Bézier functions are applied extensively in shape optimization methods. [5]
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Quantile functions are used in both statistical applications and Monte Carlo methods. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function (pdf) or probability mass function, the cumulative distribution function (cdf) and the characteristic function.