companion_matrix, a MATLAB code which computes the companion matrix for a polynomial. The polynomial may be represented in the standard monomial basis, or as a sum of Chebyshev, Gegenbauer, Hermite, Laguerre, or Lagrange basis polynomials. All the roots of the polynomial can be determined as the eigenvalues of the corresponding companion matrix.
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companion_matrix is available in a MATLAB version and an Octave version..
chebyshev_polynomial, a MATLAB code which considers the Chebyshev polynomials T(i,x), U(i,x), V(i,x) and W(i,x). Functions are provided to evaluate the polynomials, determine their zeros, produce their polynomial coefficients, produce related quadrature rules, project other functions onto these polynomial bases, and integrate double and triple products of the polynomials.
gegenbauer_polynomial, a MATLAB code which evaluates the Gegenbauer polynomial and associated functions.
hermite_polynomial, a MATLAB code which evaluates the physicist's Hermite polynomial, the probabilist's Hermite polynomial, the Hermite function, and related functions.
laguerre_polynomial, a MATLAB code which evaluates the Laguerre polynomial, the generalized Laguerre polynomial, and the Laguerre function.
legendre_polynomial, a MATLAB code which evaluates the Legendre polynomial and associated functions.
polynomial_conversion, a MATLAB code which converts representations of a polynomial between monomial, Bernstein, Chebyshev, Hermite, Laguerre and Legendre forms.
test_matrix, a MATLAB code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson matrices.