Comments on "Complete discrete 2-D Gabor transforms by neural networks for image analysis and compression

The commenters address a statement made in the above-titled paper J.G. Daugman (see ibid., vol.36, no.7, pp.1169-79, July 1988) that 'it would be completely impractical to solve this huge system of simultaneous equations by algebraic methods such as matrix manipulation, since the complexity of such methods grows factorially with the number of simultaneous equations'. They point out that the method of Gaussian elimination solves the problem in a low order polynomial time; specifically, O(N/sup 3/) arithmetic operations are needed where N is the number of linear equations and the number of unknowns. Major algorithms include LU decomposition requiring O(N/sup 3//3) operations; the Householder QR decomposition, requiring O(2N/sup 3//3) operations; and the Givens QR decomposition, requiring O(4N/sup 3/) operations.<
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