Symbolic solution of simultaneous linear algebraic equations via parallel numerical computing

An approach to the symbolic solution of simultaneous linear algebraic equations via numerical computing is described. This approach has the following attractive features: computations are inherently parallel and can be implemented on parallel processors with a fine-grain architecture, and calculations are reduced to the numerical solution of simultaneous linear equations and the fast Fourier transform (FFT). A description and mathematical substantiation of the method are given. The numerical implementation of the method on parallel computers with a fine-grain architecture is shown to be very attractive. The method is also competitive with other methods in the case of implementation on sequential computers. Numerical examples are provided to illustrate the potential of the method