Tridiagonal Coefficient Matrix
Consider the solution of Ax b by Doolittle's decomposition, where A is the n x n tridiagonal matrix As the notation implies, we are storing the nonzero elements of A in the vectors The resulting saving of storage can be significant. For example, a 100 x 100 tridiagonal matrix, containing 10,000 elements, can be stored in only 99 100 99 298 locations, which represents a compression ratio of about 33 1. Let us now apply LU decomposition to the coefficient matrix. We reduce row k by getting rid of...
