### HSL_EA20 fractional power of a sparse self-adjoint positive-deﬁnite pencil

HSL_EA20 is a suite of Fortran 95 procedures for computing the product of the s-root
of a sparse self-adjoint positive-deﬁnite matrix by a vector using a scalar
product derived by a second symmetric positive-deﬁnite matrix. Given two
$n\times n$ symmetric
positive-deﬁnite matrices $A$
and $M$, and
a vector $u$,
the package uses the Lanczos method, applied to the matrix pencil
$\left(M,A\right)$, to
approximate

$${\left({M}^{-1}A\right)}^{s}u,\phantom{\rule{1em}{0ex}}s\in \left(-1,1\right).$$

Reverse communication is used. Control is returned to the user for the products of
$A$ with
a vector $z$,
of $M$ with a
vector $x$, or
of ${M}^{-1}$ with a
vector $w$.