Determinants, norms, and the spread of circulant matrices with Tribonacci and generalized Lucas numbers
type: Item
instance of: scholarly article
title: Determinants, norms, and the spread of circulant matrices with Tribonacci and generalized Lucas numbers
zbMATH Open document ID: 1473.15013
DOI: 10.1155/2014/381829
author: Juan Li
author: Fuliang Lu
author: Zhao-Lin Jiang
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: Circulant matrices play an important role in solving ordinary and partial differential equations. In this paper, by using the inverse factorization of polynomial of degree \(n\), the explicit determinants of circulant and left circulant matrix involving Tribonacci numbers or generalized Lucas numbers are expressed in terms of Tribonacci numbers and generalized Lucas numbers only. Furthermore, four kinds of norms and bounds for the spread of these matrices are given, respectively.
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 11B39
zbMATH DE Number: 7022272
zbMATH Keywords: tribonacci numbers
zbMATH Keywords: Lucas numbers
zbMATH Keywords: determinant
Wikidata QID: Q59036982
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/381829
OpenAlex ID: W2078103917
cites work: The method of fundamental solutions for solving exterior axisymmetric Helmholtz problems with high wave-number
cites work: A circulant preconditioner for fractional diffusion equations
cites work: Energy preserving integration of bi-Hamiltonian partial differential equations
cites work: Analysis of Preconditioners for Hyperbolic Partial Differential Equations
cites work: Efficient solution of a partial integro-differential equation in finance
cites work: Circulant matrix methods for the numerical solution of partial differential equations by FFT convolutions
cites work: Discretized partial differential equations: Examples of control systems defined on modules
cites work: Observability of Discretized Partial Differential Equations
cites work: Strang-type preconditioners applied to ordinary and neutral differential-algebraic equations.
cites work: Bounded solutions of quadratic circulant difference equations
cites work: Circulant-block preconditioners for solving ordinary differential equations.
cites work: Differential equations involving circulant matrices
cites work: Chaotic image encryption algorithm based on circulant operation
cites work: APPLICATIONS OF LEFT CIRCULANT MATRICES IN SIGNAL AND IMAGE PROCESSING
cites work: Q3208805
cites work: Q5584651
cites work: Q5617667
cites work: Q5694511
cites work: On the determinants and inverses of circulant matrices with Fibonacci and Lucas numbers
cites work: Determinants and inverses of skew and skew left circulant matrices involving the \(k\)-Fibonacci numbers in communications. I
cites work: Determinants and inverses of skew and skew left circulant matrices involving the \(k\)-Lucas numbers in communications. II.
cites work: On the norms of circulant matrices with the Fibonacci and Lucas numbers
cites work: On the spectral norms of circulant matrices with classical Fibonacci and Lucas numbers entries
cites work: On the bounds for the norms of \(r\)-circulant matrices with the Fibonacci and Lucas numbers
cites work: Q3646000
cites work: Spectral norm of circulant-type matrices
cites work: The spread of a matrix
cites work: Remark on upper bounds for the spread of a matrix
cites work: Upper bounds for the spread of a matrix
cites work: Lower bounds for the spread of a matrix
cites work: Derived sequences, the Tribonacci recurrence and cubic forms
cites work: Q5404202
cites work: Q4332156
cites work: Limiting spectral distribution of a special circulant
description: scientific article; zbMATH DE number 7022272