O(N2) METHOD FOR SOLVING CONSTANT COEFFICIENT BOUNDARY-VALUE PROBLEMS IN 2 DIMENSIONS

Let M be an n**2 multiplied by n**2 block tridiagonal matrix of form M equals left bracket minus I T minus I right bracket , where T is an n multiplied by n tridiagonal matrix and I is the n multiplied by n identity. In the context of numerical computational complexity, it is shown that the system Mx equals k can be solved in O(n**2) arithmetic operations with O(n**2) storage. Numerical stability is a problem and is briefly discussed.