A fast algorithm for evaluating nth order tri-diagonal determinants

Authors:
Moawwad E. A. El-Mikkawy
Affiliations:
Mathematics Department, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
Venue:
Journal of Computational and Applied Mathematics
Year:
2004

Citing 1
Cited 2

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Abstract

The cost of all existing algorithms for evaluating the nth order determinants (Numerical Analysis, 7th Edition, Brooks & Cole Publishing, Pacific Grove, CA, 2001) is at most O(n3). In the current article we present a new efficient computational algorithm for evaluating the nth order tri-diagonal determinants with cost O(n) only. The algorithm is suited for implementation using Computer Algebra Systems such as MAPLE and MACSYMA. Some examples are given to illustrate the algorithm.