ABSTRACT: Ore deposit evaluation techniques by geostatistical simulation were first introduced some 25 years ago,, it has not fulfilled its promise as a major toot in the eartksciences. This has been largely due to two main reasons; there are some shortcomings in the method which, although recognized early on by some practitioners,, have been stow to be acknowledged and rectified, and alternatively wide usage qfkriging methods (there is although a big difference between kriging and simulation). Â survey of geostatistical simulation methods is given in Dowd (1992). Amongst proposed methods is Davis" (1987a) LU (lower and upper) decomposition method and related matrix- polynomial approximation method (Davis,, 1987b). The LU-matrix (lower and. upper) decomposition method of conditional simulation allows fast generation of stochastic processes on smallmoderate sized, grids. The method is simple and based on the LU triangular decomposition of the matrix of covariances between data, locations and simulation grid, locations (Davis, 1987a; Alabert,, 1987).. Covariances matrices are symmetric and positive-definite and therefore can be decomposed in to the product of a lower and an upper triangular matrix,. The advantages of the LU method are that it is simple to implement, performs conditioning simultaneously with simulation, is not limited to particular forms of covariance functions and handles anisotropies,. The main drawback of this method is the amount of storage required which, at least in its general form as presented,, effectively limits its application to less than 1000 grid locations. When there are many data, or when there is a large number of points on which values are to be simulated, the correspondingiy large matrices cannot he handled by classical decomposition algorithms