Polynomial

In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. Here, simple means they are constructed using only multiplication and addition. Smooth means they are infinitely differentiable, i.e., they have derivatives of all finite orders.

Related Topics:
Mathematics - Smooth - Functions - Multiplication - Addition - Derivative

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Because of their simple structure, polynomials are very easy to evaluate, and are used extensively in numerical analysis for polynomial interpolation or to numerically integrate more complex functions.

Related Topics:
Numerical analysis - Polynomial interpolation - Numerically integrate

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In linear algebra, the characteristic polynomial of a square matrix encodes several important properties of the matrix. In graph theory the chromatic polynomial of a graph encodes the different ways to vertex color the graph using x colors.

Related Topics:
Linear algebra - Characteristic polynomial - Square matrix - Matrix - Graph theory - Chromatic polynomial - Graph - Vertex color

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With the advent of computers, polynomials have been replaced by splines in many areas in numerical analysis. Splines are piecewise defined polynomials and provide more flexibility than ordinary polynomials when defining simple and smooth functions. They are used in spline interpolation and computer graphics.

Related Topics:
Computer - Spline - Piecewise - Spline interpolation - Computer graphics

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