Source of Publication
Results in Applied Mathematics
This paper analyzes the inverse of near Toeplitz pentadiagonal matrices, arising from a finite-difference approximation to the fourth-order nonlinear beam equation. Explicit non-recursive inverse matrix formulas and bounds of norms of the inverse matrix are derived for the clamped–free and clamped–clamped boundary conditions. The bound of norms is then used to construct a convergence bound for the fixed-point iteration of the form u=f(u) for solving the nonlinear equation. Numerical computations presented in this paper confirm the theoretical results.
Physical Sciences and Mathematics
Explicit formula, Finite difference, Fixed point method, Near Toeplitz, Nonlinear beam equation, Pentadiagonal matrices
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Kurmanbek, Bakytzhan; Erlangga, Yogi; and Amanbek, Yerlan, "Explicit inverse of near Toeplitz pentadiagonal matrices related to higher order difference operators" (2021). All Works. 4354.
Indexed in Scopus
Open Access Type
Hybrid: This publication is openly available in a subscription-based journal/series