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Manuscript Title: The Block Recursion Library: accurate calculation of resolvent submatrices using the block recursion method.
Authors: T.J. Godin, R. Haydock
Program title: BLOCK RECURSION LIBRARY
Catalogue identifier: ABZB_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 64(1991)123
Programming language: Fortran.
Computer: CONVEX C1.
RAM: 3K words
Word size: 32
Keywords: General purpose, Matrix, Recursion method, Resolvent, Green's functions, Schrodinger equation, Transmittance.
Classification: 4.8.

Nature of problem:
Consider a physical system, modelled by a set of coupled linear equations which are represented by a matrix M acting on a set of basis vectors. The resolvent R of M is a matrix which describes the response of the system to an applied generalized force. Often, important imformation about the solutions to the set of equations can be found from the elements of a small submatrix of R. For very large systems of equations, it is thus desirable to calculate such submatrices accurately, and without necessarily solving the full set of equations contained in M.

Solution method:
The routines in the Block Recursion Library use the block recursion method to find elements of the resolvent. This algorithm is related to the scalar recursion method. The projection of the resolvent on a pair of basis states (a two-by-two submatrix of R) is found by recursively transforming the matrix M to block-tridiagonal form, then using a matrix continued fraction constructed from the elements of the transformed matrix.

Restrictions:
The linear operator must be represented as a discrete matrix. In solid- state physics problems, for example, tight-binding models are ideally suited to this method.

Running time:
Approximately 0.5 s for sample program.