A Bound for the Inverse of a Lower Triangular Toeplitz Matrix
Copyright policy )A Bound for the Inverse of a Lower Triangular Toeplitz Matrix
The author obtains an explicit bound, namely, \(\| A_n^{-1}\| _{\infty }\leq \frac{2}{a}+\frac{1}{a_0}\) of the inverse of a lower triangular Toeplitz matrix \(A_n=(a_{ij})\) with \(a_{ij}=a_{i-j}\), inf \(a_k=a>0\), \(a_k>0\), \(a_{k+1}-a_k\leq 0\), and shows how this result can be used in the study of numerical stability of some linear methods concerning Volterra integral equations.
Volterra integral equations, Numerical methods for integral equations, inverse matrix, Toeplitz matrix, numerical stability, Miscellaneous inequalities involving matrices, norm bound, triangular matrix, recurrence formula, linear methods, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, inerse matrix
Volterra integral equations, Numerical methods for integral equations, inverse matrix, Toeplitz matrix, numerical stability, Miscellaneous inequalities involving matrices, norm bound, triangular matrix, recurrence formula, linear methods, Norms of matrices, numerical range, applications of functional analysis to matrix theory, Hermitian, skew-Hermitian, and related matrices, Theory of matrix inversion and generalized inverses, inerse matrix
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