By D. S. Mitrinovic
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Additional info for Elementary Matrices - Tutorial Text No. 3
Example text
Specifically the ARPACK package [118] is invoked. 1 Write a FORTRAN code segment to perform the matrix-vector product for matrices stored in Ellpack-Itpack format. 2 Write a small subroutine to perform the following operations on a sparse matrix in coordinate format, diagonal format, and in CSR format: a) count the number on nonzero elements in the main diagonal; b) extract the diagonal whose offset is k (which may be negative); c) add a nonzero element in position (i, j) of the matrix (assume that this position may contain a zero or a nonzero element); d) add a given diagonal to the matrix.
1 Introduction The natural idea of taking advantage of the zeros of a matrix and their location has been exploited for a long time. In the simplest situation, such as for banded or tridiagonal matrices, special techniques are straightforward to develop. , sparse matrices with irregular structure, has become popular only after the 1960’s. The main issue, and the first one to be addressed by sparse matrix technology, is to devise direct solution methods for linear systems, that are economical both in terms of storage and computational effort.
0. 10. 11. 0. 0. 0. 0. 0. 12. will be represented (for example) by AA = 12. 9. 7. 5. 1. 2. 11. 3. 6. 4. 8. 10. JR = 5 3 3 2 1 1 4 2 3 2 3 4 JC = 5 5 3 4 1 4 4 1 1 2 4 3 In the above example we have, on purpose, listed the elements in an arbitrary order. In fact it would have been more natural to list the elements by row or columns. If we listed the elements row-wise, we would notice that the array JC Chapter 2 32 contains redundant information, and may be replaced by an array that points to the beginning of each row instead.