Positive integer powers and inverse for one type of even order symmetric pentadiagonal matrices
نویسندگان
چکیده
In this study we derive the general expression for the entries of the qth power (q 2 N) for one type of even order symmetric pentadiagonal matrices.
منابع مشابه
On the Inverse Problem of Constructing Symmetric Pentadiagonal Toeplitz Matrices from Three Largest Eigenvalues
The inverse problem of constructing a symmetric Toeplitz matrix with prescribed eigenvalues has been a challenge both theoretically and computationally in the literature. It is now known in theory that symmetric Toeplitz matrices can have arbitrary real spectra. This paper addresses a similar problem — Can the three largest eigenvalues of symmetric pentadiagonal Toeplitz matrices be arbitrary? ...
متن کاملProperties of Central Symmetric X-Form Matrices
In this paper we introduce a special form of symmetric matrices that is called central symmetric $X$-form matrix and study some properties, the inverse eigenvalue problem and inverse singular value problem for these matrices.
متن کاملEigenvalues of Hadamard powers of large symmetric Pascal matrices
Let Sn be the positive real symmetric matrix of order n with (i, j ) entry equal to ( i + j − 2 j − 1 ) , and let x be a positive real number. Eigenvalues of the Hadamard (or entry wise) power S n are considered. In particular for k a positive integer, it is shown that both the Perron root and the trace of S n are approximately equal to 4 4k−1 ( 2n− 2 n− 1 )k . © 2005 Elsevier Inc. All rights r...
متن کاملRecurrence Relations between Symmetric Polynomials of n-th Order
The method of symmetric polynomials (MSP) was developed for computation analytical functions of matrices, in particular, integer powers of matrix. MSP does not require for its realization finding eigenvalues of the matrix. A new type of recurrence relations for symmetric polynomials of order n is found. Algorithm for the numerical calculation of high powers of the matrix is proposed.This comput...
متن کاملSome Preconditioners for Block Pentadiagonal Linear Systems Based on New Approximate Factorization Methods
In this paper, getting an high-efficiency parallel algorithm to solve sparse block pentadiagonal linear systems suitable for vectors and parallel processors, stair matrices are used to construct some parallel polynomial approximate inverse preconditioners. These preconditioners are appropriate when the desired target is to maximize parallelism. Moreover, some theoretical results about these pre...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Applied Mathematics and Computation
دوره 219 شماره
صفحات -
تاریخ انتشار 2013