3d. Sparse Matrix Methods We want to solve where is large, sparse, and By sparse, is nearly Ax=b, A NN. A all zeroes. Consider the tridiagonal matrix, . If then is sparse, but if N=10,000, A it is not sparse. Typical sparse matrices are not just banded or diagonal N=4 matrices. The nonzero pattern may appear to be random at first glance. There are a small number of common storage schemes so that (almost) no zeroes are stored for ideally storing only = number of nonzeroes in A, NZ(A) A: Diagonal (or band) Profile
3d. Sparse Matrix Methods We want to solve Ax=b, where A is large, sparse, and NN. By sparse, A is nearly all zeroes. Consider the tridiagonal matrix, . If N=10,000, then A is sparse, but if N=4 it is not sparse. Typical sparse matrices are not just banded or diagonal matrices. The nonzero pattern may appear to be random at first glance. There are a small number of common storage schemes so that (almost) no zeroes are stored for A, ideally storing only NZ(A) = number of nonzeroes in A: Diagonal (or band) Profile
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