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Start Over Subject Toeplitz matrix

1. An iterative algorithm for computing the cycle mean of a Toeplitz matrix in special form

Creator:
Szabö, Peter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
max-plus algebra, eigenvalue, sub-partition of an integer, and Toeplitz matrix
Language:
English
Description:
The paper presents an iterative algorithm for computing the maximum cycle mean (or eigenvalue) of n×n triangular Toeplitz matrix in max-plus algebra. The problem is solved by an iterative algorithm which is applied to special cycles. These cycles of triangular Toeplitz matrices are characterized by sub-partitions of n−1.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Noncirculant Toeplitz matrices all of whose powers are Toeplitz

Creator:
Griffin, Kent, Stuart, Jeffrey L., and Tsatsomeros, Michael J.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
Toeplitz matrix, Toeplitz inverse, Toeplitz powers, principal minor, and Fibonacci sequence
Language:
English
Description:
Let $a$, $b$ and $c$ be fixed complex numbers. Let $M_n(a,b,c)$ be the $n\times n$ Toeplitz matrix all of whose entries above the diagonal are $a$, all of whose entries below the diagonal are $b$, and all of whose entries on the diagonal are $c$. For $1\leq k\leq n$, each $k\times k$ principal minor of $M_n(a,b,c)$ has the same value. We find explicit and recursive formulae for the principal minors and the characteristic polynomial of $M_n(a,b,c)$. We also show that all complex polynomials in $M_n(a,b,c)$ are Toeplitz matrices. In particular, the inverse of $M_n(a,b,c)$ is a Toeplitz matrix when it exists.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public