This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the properties of the inverse of the related pentadiagonal matrices, associated with the fourth-order nonlinear beam equation. This nonlinear problem is discretized using the finite difference method with the clamped-free and clamped-clamped boundary conditions in the one dimension. Explicit formulas for the inverse of the matrices and norms of the inverse are derived. In iterative process, the direct computation of inverse matrix allows to achieve an efficiency. Numerical results were provided.

翻译：本文件分析了与第四级非线性光束等式相关的表u=f(u)的固定点迭代和相关的五边形矩阵反面特性的趋同性。这个非线性问题使用有限差异法与一个维度的无夹和夹紧的边界条件分解。得出了反面矩阵和反面规范的明显公式。在迭接过程中,直接计算反面矩阵可以提高效率。提供了数字结果。