Download Computational Methods for General Sparse Matrices by Zahari Zlatev (auth.) PDF

By Zahari Zlatev (auth.)

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Assume that the number of elements of matrix A that are not small is NZl. It is clear that NZl ~ NZ. The ALU and CNLU should be NN ~ 2*NZ1 and the length of length of arrays NNl ~ NZl when the computer-oriented manner is array RNLU should be applied, while the corresponding lengths should satisfy NN ~ 2*NZ and NNl when the classical manner of exploiting the sparsity is used. In some ~ NZ cases NZl is considerably smaller than NZ. This is so for the problems ar~s~ng in nuclear magnetic resonance spectroscopy ([336,337]).

E. the non-zero elements of matrix A, together with their row and column numbers, are stored (in an arbitrary order) in arrays AORIG, RNORIG and CNORIG respectively. After the second step the number of non-zeros in row i is stored in HA(i,3), while the number of non-zeros in column j is stored in HA(j,6). • During the third step of the initialization of the dynamic storage scheme the positions of the row starts in the row ordered list and the column starts in the column ordered list are determined.

The experiment shows that a good compromise is to allow a small number of garbage collections. It must be emphasized here that no problems with garbage collections arise when this particular system is solved using the computer-oriented manner of exploiting sparsity. 2 Comparison of the choice of the lengths of the main arrays (NN and NNl) and the number of garbage collections ( 0 GC in ROL 0 and 0 GC in COL" are abbreviations for garbage collections in the row ordered list and garbage collections in the column ordered list respectively).

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