Error estimation formula for FWT-based solvers for dense linear equations

We present an error estimation formula for the FWT-based solvers of a class of dense linear equations, especially those arising from the numerical resolution of some kind of integral equations. The estimation is a priori under the condition mat the transformed right-hand sides of the problem under consideration belong to the Lp k (Ã) space defined in this paper. Since the estimation is associated with the degree of freedom of the linear system and the threshold used in the FWT-based solver, it provides a clue to determining the value of the threshold such that the corresponding approximate solution has a desired accuracy. In addition, sufficient conditions are found for the related p-expanding matrices with order k. The proposed theory is validated by numerical test.