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 \(\mathbf{A}\) and \(\mathbf{M}\), and a vector \(\mathbf{u}\), the package uses the Lanczos method, applied to the matrix pencil \((\mathbf{M} , \mathbf{A})\), to approximate \[\left( \mathbf{M}^{-1}\mathbf{A}\right)^s \mathbf{u} , \quad s\in (-1,1).\]

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