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).