Abstract
The quadtrees matrix representation has been recently proposed as an alternative to the conventional linear storage of matrices. If all elements of a matrix are zero, then the matrix is represented by an empty tree; otherwise it is represented by a tree consisting of four subtrees, each representing, recursively, a quadrant of the matrix. Using four-way block decomposition, algorithms on quadtrees accelerate on blocks entirely of zeroes, and thereby offer improved performance on sparse matrices. This paper reports the results of experiments done with a quadtree matrix package implemented in REDUCE to compare the performance of quadtree representation with REDUCE's built-in sequential representation of matrices. Tests on addition, multiplication, and inversion of dense, triangular, tridiagonal, and diagonal matrices (both symbolic and numeric) of sizes up to 100×100 show that the quadtree algorithms perform well in a broad range of circumstances, sometimes running orders of magnitude faster than their sequential counterparts.
isiting scientist at Tektronix Labs during the summer of 1987 when this work was done.
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Abdali, S.K., Wise, D.S. (1989). Experiments with quadtree representation of matrices. In: Gianni, P. (eds) Symbolic and Algebraic Computation. ISSAC 1988. Lecture Notes in Computer Science, vol 358. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51084-2_9
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DOI: https://doi.org/10.1007/3-540-51084-2_9
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