Version 1.1.0
18th July 2013 User documentation
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HSL_EA20: fractional power of a sparse selfadjoint positivedefinite pencil
HSL_EA20
is a suite of FortranĀ 95 procedures for computing the product of the sroot of a sparse selfadjoint positivedefinite matrix by a vector using a scalar product derived by a second symmetric positivedefinite matrix. Given two \(n\times n\) symmetric positivedefinite 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 \(\mathbf{w}\).