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[Licence| Download | New Version Template] aali_v1_0.gz(11 Kbytes)
Manuscript Title: Matrix linearization.
Authors: L. Seijo, M. Florez, L. Pueyo
Program title: LINRZ
Catalogue identifier: AALI_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 42(1986)127
Programming language: Fortran.
Computer: HP 1000/45F.
Operating system: RTE-6/VM.
RAM: 44K words
Word size: 16
Peripherals: disc.
Keywords: General purpose, Fit, Matrix linearization, Inverse eigenvalue Problem, Spectral parameters.
Classification: 4.8, 4.9.

Nature of problem:
Given a Hermitian matrix H, with matrix elements defined as linear combinations of a set of adjustable parameters, the program computes the eigenvalues of H and the corresponding parameters that best reproduce a set of known numbers.

Solution method:
The eigenvalues Ei of a Hermitian matrix H with matrix elements Hij = Sigma k A**k ij ak, where A**k ij are known numbers and ak a set of adjustable parameters, are expressed as Ei = Sigma k (Delta Ei/Delta ak) ak. Starting with a trial set of ak's the partial derivatives are calulated algebraically. Then, an improved set of parameters is found by linear least squares fitting over the given data. The process is iterated until convergence.

Restrictions:
Only Hermitian matrices can be considered. Their matrix elements must be linear on the parameters.

Unusual features:
The program can be run in BATCH mode or interactively. When running interactively, the program displays information on the iterative process, and allows the user to modify the eigenvalue-data assignment during the execution.

Running time:
8 s for the test run (with two cases)