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A C++ Program for testing a Matrix For Sparsity and Diagonalization
Abstract
Matrices are used extensively in both linear algebra and differential equations. Often times, processing a matrix can be very time consuming. The processing can often prove to be more computationally efficient if it is known if the matrix has a certain structure. If it can be determined that a matrix has such a structure, more efficient algorithms can then be developed to process the matrix. In this paper, source code is presented to preprocess a matrix to determine if the matrix is sparse and to test for the diagonalization, the number of diagonals with the same number of diagonals above and below the main diagonal. If this structure can be determined, new algorithms can be written to make the computational complexity of processing the matrix more effective and efficient.
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