On the statistical properties of solutions of completely random linear systems
Peter Sonneveld · Research Repository (Delft University of Technology) · 2010
In this report the probability distributions of x and kxk are derived, where x is the solution of a finite square, completely random linear system, i.e. a system Ax = b, of which all entries are stochastically independent, and standard Gaussian distributed stochastic variables. The question on the statistical behaviour of kxk came up in [5], the convergence analysis of IDR(s), which is a recently developed, short-recurrence Krylov subspace based iterative solution method for large sparse non-symmetric linear systems of equations, ([6], [4]).