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Manuscript Title: The recursion method: processing the continued fraction.
Authors: C.M.M. Nex
Program title: RECLIB
Catalogue identifier: ACDL_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 34(1984)101
Programming language: Fortran.
Operating system: MICROSOFT FORTRAN, CP/M-80.
RAM: 37K words
Word size: 8
Keywords: General purpose, Other numerical, Liquid, Density of states, Recursion method, Fermi energy, Continued fraction, Jacobi matrix, Recurrence relation, Tridiagonal matrix, Gaussian quadrature, Orthogonal polynomials, Eigenvalues, Terminator.
Classification: 4.12.

Nature of problem:
Calculation of the local density of states and related quantities from the tridiagonalisation, or continued fraction, generated through the application of the recursion method. This may be for electronic or vibrational properties of any of the essentially locally interacting systems for which the recursion method is an appropriate way to solve the Schrodinger equation, i.e. in which nearer neighbour interactions dominate.

Solution method:
In a library of routines we provide three different termination techniques appropriate for different circumstances: the 'square root terminator' as originally suggested, the generalization of this to several bands and the quadrature approach. A fermi energy calculator is included, inverting the integrated density of states function, and also an algorithm for matching between a given continued fraction and a 'model' analytic one. Classical algorithms are applied to the problems in linear algebra and orthogonal polynomials which arise in this work.

The local density of states must be a positive function on some subset of the real line. Local machine speed will determine the maximum length of the continued fraction; store is not a significant problem.

Unusual features:
The independent routine structure gives the user control and great flexibility in the application of sophisticated mathematical techniques.

Running time:
Of order ten min on the Advantage and of order two s on the IBM 3081.