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Manuscript Title: Fast eigensolver for dense real-symmetric matrices.
Authors: C.F. Bunge
Program title: HQRII1
Catalogue identifier: ADOP_v1_0
Distribution format: gz
Journal reference: Comput. Phys. Commun. 138(2001)92
Programming language: Fortran.
Computer: PCs, desktops, workstations, supercomputers.
Operating system: Linux, UNICOS, DEC Unix, Irix.
Word size: 64
Keywords: Benchmark, Eigenproblem, Eigenvalue, Eigenvector, LAPACK, Linear algebra, Matrix, Real symmetric matrices, Cisc processor, Risc processor, Vector processor, General purpose.
Classification: 4.8.

Nature of problem:
Solving eigenproblems is a widespread technique in engineering and basic sciences, as manifested by more than 400 paper titles carrying the word eigenvalue or eigenvector in the last two years.

Solution method:
An input real-symmetric matrix A is tridiagonalized by the method of Householder. The eigenvalues of the tridiagonal matrix T are found by the QR method with origin shift. Optionally, some or all eigenvectors of matrix T are determined by inverse iteration. The eigenvectors of matrix A are found by left-multiplying the eigenvectors of matrix T times the orthogonal matrix which brings A to tridiagonal form. The high speed storage required is approximately 3/2 * N**2 + 21 * N double precision words, where N is the matrix dimension.

Running time:
4475 elapsed seconds for all eigenvalues and eigenvectors of a matrix of order 8000 (Compaq Alpha 21264A, 667 MHz).