Polynomials

Curve fitting, roots, partial fraction expansions

Polynomials are equations of a single variable with nonnegative integer exponents. MATLAB^® represents polynomials with numeric vectors containing the polynomial coefficients ordered by descending power. For example, [1 -4 4] corresponds to x² - 4x + 4. For more information, see Create and Evaluate Polynomials.

Functions

`poly`	Polynomial with specified roots or characteristic polynomial
`polydiv`	Polynomial long division (Since R2024a)
`polyeig`	Polynomial eigenvalue problem
`polyfit`	Polynomial curve fitting
`residue`	Partial fraction expansion (partial fraction decomposition)
`roots`	Polynomial roots
`polyval`	Polynomial evaluation
`polyvalm`	Matrix polynomial evaluation
`conv`	Convolution and polynomial multiplication
`deconv`	Least-squares deconvolution and polynomial division
`polyint`	Polynomial integration
`polyder`	Polynomial differentiation

Topics

Create and Evaluate Polynomials
This example shows how to represent a polynomial as a vector in MATLAB® and evaluate the polynomial at points of interest.
Roots of Polynomials
Calculate polynomial roots numerically, graphically, or symbolically.
Integrate and Differentiate Polynomials
This example shows how to use the polyint and polyder functions to analytically integrate or differentiate any polynomial represented by a vector of coefficients.
Polynomial Curve Fitting
This example shows how to fit a polynomial curve to a set of data points using the polyfit function.
Programmatic Fitting
There are many functions in MATLAB that are useful for data fitting.

Featured Examples

Predicting the US Population

Extrapolating data using polynomials of even modest degree is risky and unreliable.

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