By Ellis Horowitz

This article deals a whole rendering of simple facts constitution implementations within the well known language C++.

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LOC(a31) = 1, LOC(a42) = 2 in the example above. 56 EXERCISES EXERCISES 57 15. A generalized band matrix An,a,b is a n x n matrix A in which all the nonzero terms lie in a band made up of a - 1 diagonals below the main diagonal, the main diagonal and b - 1 diagonals above the main diagonal (see the figure on the next page) a) How many elements are there in the band of An,a,b? b) What is the relationship between i and j for elements aij in the band of An,a,b? c) Obtain a sequential representation of the band of An,a,b in the one dimensional array B.

Then the following program is produced. 3 SPARSE MATRICES The author of this procedure has declared 101 * 203 = 20,503 locations to hold the Fibonacci polynomials, which is about twice as much as is actually needed. A much greater saving could be achieved if Fi(x) were printed as soon as it was computed in the first loop. Then by storing all polynomials in a single array, 1000 locations would be more than adequate. However, storing several polynomials in a single array alters the way one creates new polynomials and complicates matters if they are to be destroyed and the space reused.

17. 3 for sparse matrix representation involves representing only the non zero terms in a one dimensional array VA in the order described. In addition, a strip of n x m bits, BA (n,m), is also kept. BA(i,j) = 0 if A(i,j) = 0 and BA(i,j) = 1 if A(i,j) 0. 1. (i) On a computer with w bits per word, how much storage is needed to represent a sparse matrix Anxm with t nonzero terms? (ii) Write an algorithm to add two sparse matrices A and C represented as above to obtain D = A + C. How much time does your algorithm take ?