Experiments with quadtree representation of matrices

  • S. Kamal Abdali
  • David S. Wise
Part of the Lecture Notes in Computer Science book series (LNCS, volume 358)


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.

CR categories and subject descriptors

I.1.2 [Algebraic Manipulation Algorithms]; Algebraic algorithms E.1 [Data Structures]: Trees G.1.3 [Numerical Linear Algebra]: Sparse and very large systems General Term: Measurement 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • S. Kamal Abdali
    • 1
  • David S. Wise
    • 2
  1. 1.Tektronix LabsBeavertonUSA
  2. 2.Indiana UniversityBloomingtonUSA

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