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

By Zahari Zlatev (auth.)

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5). e. before the beginning of the GE process), are needed. These extra locations form the so-called elbow room in the main arrays of the dynamic storage scheme. It is very important to determine how many locations are needed for elbow room. Unfortunately, the number of these locations depends on the number of fill-ins created during the GE (or, more generally, on the particular method used to decompose matrix A) and therefore is not known before the start of the computations. Experiments carried out with several thousands of matrices indicated that as a rule the choice NNE [SNZ,lONZ] is a good one when the classical manner of exploiting sparsity is in use.

In this experiment NN = COUNT + kN and NNl = COUNTl + kN with k=2(2)32 is used (the values of COUNT and COUNTl were found in the previous experiment: COUNT=49023 and COUNT1=27427). For k=2,4, 6 the number of garbage collections is very large. For k>lO the number of garbage collections is quite reasonable. However, k must be large if one wants to avoid garbage collections. Garbage collections in the column ordered list are avoided for NNl = GOUNTl + 32N = 59149. The smallest number NN for which garbage collections in the row ordered list can be avoided has not been found (for NN = 99999 the code performed one garbage collection.

It is said that ALU, CNLU and the first three columns of HA form Chapter 2 16 the row ordered list or the row-oriented structure. In the second group of arrays the row numbers of the elements in matrix A are ordered by columns in array RNLU; some pointers concerning this structure are given in the next three columns of array HA. It is said that RNLU together with the fourth, the fifth and the sixth columns of HA form the column ordered list or the column-oriented structure. 4. The dynamic storage scheme discussed here is designed for GE with transformations carried out by rows.

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