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MatrixPolynomials.jl

The main purpose of this package is to provide polynomial approximations to $f(\mat{A})$, i.e. the function of a matrix $\mat{A}$ for which the field-of-values $W(\mat{A}) \subset \Complex$ (or equivalently the distribution of eigenvalues) is known a priori. If this is the case, a polynomial approximation $p(z) \approx f(z)$ for $z \in W(\mat{A})$ can be constructed, and this can subsequently be used, substituting $\mat{A}$ for $z$. This is in contrast to Krylov-based methods, where the matrix polynomials are generated on-the-fly, without any prior knowledge of $W(\mat{A})$ (even though knowledge can be used to speed up the convergence of the Krylov iterations).

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