A Class of Asynchronous Block Methods for Nonlinear Systems of Equations

The authors investigate nonlinear systems of equation represented by F(X) = 0 (1.1) where F = (f{sub 1}, ..., f{sub n}){sup T}, is a nonlinear operator from R{sup n} into itself, and X = (x{sub 1},...,x{sub n}){sup T}. To design a parallel algorithm for (1.1), we partition F and x as follows: F = (F{sup T}{sub 1},...,F{sup T}{sub 1}){sup T}, X = (X{sup T}{sub 1},...,X{sup T}{sub 1}){sup T} where F{sub 1} = (f{sub il},...,f{sub ini}){sup T}, X{sub i} = (x{sub il},...,x{sub ini}){sup T}, i = 1,...,l. Let S{sub i} = (il,...,in{sub i}), then US{sub i} = (1,...,n), Si {intersection} S{sub j} + {var_phi}, i = j, i, j = 1,...,l.