Inexact overlapped block Broyden methods for solving nonlinear equations
The paper is concerned with the problem of solving a large system of nonlinear equations. Many methods are suitable for this: Newton methods, inexact Newton methods, nonlinear block-iterative methods, inexact Newton-Krylov methods, etc. The authors discuss the inexact Broyden method with partially overlap which is a generalization of the parallelizable Jacobi-type block Broyden method. By directly performing the block Broyden iteration for the overlapped blocks and by assembling the overlapping parts of the results into an average weighted manner at each iteration, the block Broyden method is accelerated. A new algorithm which is a generalization of the block Broyden method with partially overlapped blocks is presented and the local convergence of this algorithm is proved. The implementation of the algorithm by several strategies for partitioning the Jacobian into weakly coupled partially ovelapped blocks is discussed and one numerical example (a system of \(N\) nonlinear equations) is performed by ten variants of the iterations.
scientific article; zbMATH DE number 1861383
scientific article