This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, w... more This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.
We present a proof of determinant of special nonsymmetric Toeplitz matrices conjectured by Anelić... more We present a proof of determinant of special nonsymmetric Toeplitz matrices conjectured by Anelić and Fonseca in <cit.>. A proof is also demonstrated for a more general theorem. The two conjectures are therefore just two possible results, under two specific settings. Numerical examples validating the theorem are provided.
This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the proper... more 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 fourthorder 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.
This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, w... more This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.
In this short note, we provide a brief proof for a recent determinantal formula involving a parti... more In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.
This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, w... more This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.
We present a proof of determinant of special nonsymmetric Toeplitz matrices conjectured by Anelić... more We present a proof of determinant of special nonsymmetric Toeplitz matrices conjectured by Anelić and Fonseca in <cit.>. A proof is also demonstrated for a more general theorem. The two conjectures are therefore just two possible results, under two specific settings. Numerical examples validating the theorem are provided.
This paper analyzes the convergence of fixed-point iterations of the form u = f(u) and the proper... more 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 fourthorder 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.
This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, w... more This paper presents the explicit inverse of a class of seven-diagonal (near) Toeplitz matrices, which arises in the numerical solutions of nonlinear fourth-order differential equation with a finite difference method. A non-recurrence explicit inverse formula is derived using the Sherman-Morrison formula. Related to the fixed-point iteration used to solve the differential equation, we show the positivity of the inverse matrix and construct an upper bound for the norms of the inverse matrix, which can be used to predict the convergence of the method.
In this short note, we provide a brief proof for a recent determinantal formula involving a parti... more In this short note, we provide a brief proof for a recent determinantal formula involving a particular family of banded matrices.
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