Matrix algebra and applicative programming

fast Fourier transform. Abstract The broad problem of matrix algebra is taken up from the perspective of functional programming. A key question is how arrays should be represented in order to admit good implementations of well-known eecient algorithms, and whether functional architecture sheds any new light on these or other solutions. It relates directly to disarming the \ag-gregate update" problem. The major thesis is that 2 d-ary trees should be used to represent d-dimensional arrays; examples are matrix operations (d = 2), and a particularly interesting vector (d = 1) algorithm. Sparse and dense matrices are represented homogeneously, but at some overhead * c 1987 by Springer-Verlag. (1987) 134{153. The two appendices that are omitted here are available there.