Fast eigensolver for dense real-symmetric matrices. C.F. Bunge.

PROGRAM SUMMARY
Title of program: HQRII1
Catalogue identifier: ADOP
Ref. in CPC: 138(2001)92
Distribution format: gzip file
Operating system: Linux, UNICOS, DEC Unix, Irix
Number of bits in a word: 64
Number of lines in distributed program, including test data, etc: 7841
Keywords: Benchmark, Eigenproblem, Eigenvalue, Eigenvector, LAPACK, Linear algebra, Matrix, Real symmetric matrices, Cisc processor, Risc processor, Vector processor, General purpose.
Programming language used: Fortran
Computer: PCs , desktops , workstations , supercomputers .

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.

Method of solution:
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.

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