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By P. Antognetti, Donald O. Pederson and Hugo De Man (Editors)

ISBN-10: 9028627014

ISBN-13: 9789028627017

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Additional resources for Computer Design Aids for VLSI Circuits (NATO ASI (Advanced Science Institutes) Series E Applied Sciences - No. 48)

Example text

This data structure is particularly efficient for sparse matrices algorithms. For example, after an element not on the main diagonal has been selected, a row and column interchange is required. To swap two rows, we only need to redirect the corresponding pointers in IIPT. We also need to change the IROW 53 -i 0 0 -j 0 0 0 0 ROW 3 7 4 2 ROW 4 -13413 1 Figure 11a. The bidirectional threaded list. 4 4 ] (A. Figure 11b. The FORTRAN oriented implementation of the bidirectional threaded list. 54 entries corresponding to the elements in the swapped rows.

N. However, during GE we may encounter an entry akk which is zero. For example, consider the system x 1 + x 2 + x 3 =1/2 x 1 + x 2 +3x 3 =2 x 1 +3x 2 +3x 3 =1 which has solution x 1 =1/4,x first step of GE we have 2 =1/2,x 3 =3/4. After the 0x2+2x3=3/4 2x 2 +2x 3=1/2 where(2) a 22 =0. A way of overcoming this difficulty is w to interchange rows and/or columns. In fact, if we interchange row 2 and 3, then the new system has a nonzero element where needed by GE. In the general case, when a(k)= 0 one might ask whether by interchanging row k with row r, r>k, we can continue GE.

This implies that we need 36 multiplications to obtain the solution of the system A'x=b with no advantage with respect to the full matrix case. This example shows that the number of nontrivial operations required to solve Ax=b when A is sparse, depends upon the row and column permutations of the coefficient matrix. is obvious that we should find a In general, it permutation of A for which GE or LU decomposition re- 49 quires the minimum number of multiplications. Another criterion which can be followed in the selection of the permutation of A is the minimization of the number of nonzero elements created in A during GE.

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Computer Design Aids for VLSI Circuits (NATO ASI (Advanced Science Institutes) Series E Applied Sciences - No. 48) by P. Antognetti, Donald O. Pederson and Hugo De Man (Editors)


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