BOUNDS FOR THE MAXIMUM EIGENVALUES OF THE FIBONACCI-FRANK AND LUCAS-FRANK MATRICES

被引：2

作者：

Mersin, Efruz Ozlem ^{[1
]}

Bahsi, Mustafa ^{[2
]}

机构：

[1] Aksaray Univ, Dept Math, Aksaray, Turkiye

[2] Aksaray Univ, Dept Math & Sci Educ, Aksaray, Turkiye

来源：

COMMUNICATIONS FACULTY OF SCIENCES UNIVERSITY OF ANKARA-SERIES A1 MATHEMATICS AND STATISTICS | 2024年 / 73卷 / 02期

关键词：

Fibonacci sequence; Lucas sequence; Frank matrix; eigenvalue; bounds; norm; CIRCULANT MATRICES; STURM SEQUENCES; NORMS; THEOREM;

D O I：

10.31801/cfsuasmas.1299736

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

. Frank matrix is one of the popular test matrices for eigenvalue routines because it has well-conditioned and poorly conditioned eigenvalues. In this paper, we investigate the bounds for the maximum eigenvalues of the special cases of the generalized Frank matrices which are called FibonacciFrank and Lucas-Frank matrices. Then, we obtain the Euclidean norms and the upper bounds for the spectral norms of these matrices.

引用

页码：420 / 436

页数：17

共 24 条

[1] [Anonymous], 1965, The Algebraic Eigenvalue Problem
[2] [Anonymous], 1970, Die Grundlehren der mathematischen Wissenschaften
[3] Bahsi M, 2015, TWMS J PURE APPL MAT, V6, P84
[4] DUPREE E., 2012, Int. J. Contemp. Math. Science., V7, P2327
[5] COMPUTING EIGENVALUES OF COMPLEX MATRICES BY DETERMINANT EVALUATION AND BY METHODS OF DANILEWSKI AND WIELANDT
FRANK, WL
[J]. JOURNAL OF THE SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS, 1958, 6 (04): : 378 - 392
[6] STURM SEQUENCES FOR NONLINEAR EIGENVALUE PROBLEMS
GREENBERG, L
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1989, 20 (01) : 182 - 199
[7] A REMARK ON FRANK MATRICES
HAKE, JF
[J]. COMPUTING, 1985, 35 (3-4) : 375 - 379
[8] Horn R. A., 1985, Matrix Analysis, DOI [10.1017/CBO9780511810817, DOI 10.1017/CBO9780511810817]
[9] Jafari-Petroudi S. H., 2016, International Journal of Advances in Applied Mathematics and Mechanics, V3, P82
[10] Koshy T., 2001, Fibonacci and Lucas Numbers With Applications

← 1 2 3 →