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Journal articles on the topic 'Tridiagonal matrices'

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Published: 10 September 2021
Last updated: 25 April 2022

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1

Newman, Morris. "Tridiagonal matrices." Linear Algebra and its Applications 201 (April 1994): 51–55. http://dx.doi.org/10.1016/0024-3795(94)90103-1.

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2

Pan, Hongyan, and Zhaolin Jiang. "VanderLaan Circulant Type Matrices." Abstract and Applied Analysis 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/329329.

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Circulant matrices have become a satisfactory tools in control methods for modern complex systems. In the paper, VanderLaan circulant type matrices are presented, which include VanderLaan circulant, left circulant, andg-circulant matrices. The nonsingularity of these special matrices is discussed by the surprising properties of VanderLaan numbers. The exact determinants of VanderLaan circulant type matrices are given by structuring transformation matrices, determinants of well-known tridiagonal matrices, and tridiagonal-like matrices. The explicit inverse matrices of these special matrices are obtained by structuring transformation matrices, inverses of known tridiagonal matrices, and quasi-tridiagonal matrices. Three kinds of norms and lower bound for the spread of VanderLaan circulant and left circulant matrix are given separately. And we gain the spectral norm of VanderLaang-circulant matrix.
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3

Barreras, A., and J. M. Peña. "Tridiagonal M-matrices whose inverse is tridiagonal and related pentadiagonal matrices." Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 113, no. 4 (June 27, 2019): 3785–93. http://dx.doi.org/10.1007/s13398-019-00707-3.

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4

Yuan, Shifang, Anping Liao, and Yuan Lei. "Inverse eigenvalue problems of tridiagonal symmetric matrices and tridiagonal bisymmetric matrices." Computers & Mathematics with Applications 55, no. 11 (June 2008): 2521–32. http://dx.doi.org/10.1016/j.camwa.2007.10.006.

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5

Perline, Ronald. "Toeplitz Matrices and Commuting Tridiagonal Matrices." SIAM Journal on Matrix Analysis and Applications 12, no. 2 (April 1991): 321–26. http://dx.doi.org/10.1137/0612023.

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6

Dahl, Geir. "Tridiagonal doubly stochastic matrices." Linear Algebra and its Applications 390 (October 2004): 197–208. http://dx.doi.org/10.1016/j.laa.2004.04.017.

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7

Beiranvand, Mohammad, and Mojtaba Ghasemi Kamalvand. "Explicit Expression for Arbitrary Positive Powers of Special Tridiagonal Matrices." Journal of Applied Mathematics 2020 (September 12, 2020): 1–5. http://dx.doi.org/10.1155/2020/7290403.

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8

Fu, Yaru, Xiaoyu Jiang, Zhaolin Jiang, and Seongtae Jhang. "Analytic determinants and inverses of Toeplitz and Hankel tridiagonal matrices with perturbed columns." Special Matrices 8, no. 1 (May 4, 2020): 131–43. http://dx.doi.org/10.1515/spma-2020-0012.

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AbstractIn this paper, our main attention is paid to calculate the determinants and inverses of two types Toeplitz and Hankel tridiagonal matrices with perturbed columns. Specifically, the determinants of the n × n Toeplitz tridiagonal matrices with perturbed columns (type I, II) can be expressed by using the famous Fibonacci numbers, the inverses of Toeplitz tridiagonal matrices with perturbed columns can also be expressed by using the well-known Lucas numbers and four entries in matrix 𝔸. And the determinants of the n×n Hankel tridiagonal matrices with perturbed columns (type I, II) are (−1]) {\left( { - 1} \right)^{{{n\left( {n - 1} \right)} \over 2}}} times of the determinant of the Toeplitz tridiagonal matrix with perturbed columns type I, the entries of the inverses of the Hankel tridiagonal matrices with perturbed columns (type I, II) are the same as that of the inverse of Toeplitz tridiagonal matrix with perturbed columns type I, except the position. In addition, we present some algorithms based on the main theoretical results. Comparison of our new algorithms and some recent works is given. The numerical result confirms our new theoretical results. And we show the superiority of our method by comparing the CPU time of some existing algorithms studied recently.
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9

YALÇINER, AYNUR. "THE LU FACTORIZATIONS AND DETERMINANTS OF THE K-TRIDIAGONAL MATRICES." Asian-European Journal of Mathematics 04, no. 01 (March 2011): 187–97. http://dx.doi.org/10.1142/s1793557111000162.

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10

Fan, Hong Ling. "Fast Algorithm for the Inverse Matrices of Periodic Adding Element Tridiagonal Matrices." Advanced Materials Research 159 (December 2010): 464–68. http://dx.doi.org/10.4028/www.scientific.net/amr.159.464.

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Adding element tridiagonal periodic matrices have an important effect for the algorithms of solving linear systems，computing the inverses, the triangular factorization，the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.
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11

Zhao, Yan Lei, and Xue Ting Liu. "Fast Algorithm for the Inverse Matrices of Adding Element Tridiagonal Periodic Matrices in Signal Processing." Advanced Materials Research 121-122 (June 2010): 682–86. http://dx.doi.org/10.4028/www.scientific.net/amr.121-122.682.

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Adding element tridiagonal matrices play a very important role in the theory and practical applications, such as the boundary value problems by finite difference methods, interpolation by cubic splines, three-term difference equations and so on. In this paper, we give a fast algorithm for the Inverse Matrices of periodic adding element tridiagonal matrices.
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12

Dong, Chuan Dai. "Estimates for the Lower Bounds on the Inverse Elements of Strictly Diagonally Dominant Tridiagonal Matrices in Signal Processing." Advanced Materials Research 121-122 (June 2010): 929–33. http://dx.doi.org/10.4028/www.scientific.net/amr.121-122.929.

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In the theory and practical applications, tridiagonal matrices play a very important role. In this paper, Motivated by the references, especially [2], we give the estimates for the lower bounds on the inverse elements of strictly diagonally dominant tridiagonal matrices.
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13

Altun, Muhammed. "Fine Spectra of Symmetric Toeplitz Operators." Abstract and Applied Analysis 2012 (2012): 1–14. http://dx.doi.org/10.1155/2012/932785.

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The fine spectra of 2-banded and 3-banded infinite Toeplitz matrices were examined by several authors. The fine spectra ofn-banded triangular Toeplitz matrices and tridiagonal symmetric matrices were computed in the following papers: Altun, “On the fine spectra of triangular toeplitz operators” (2011) and Altun, “Fine spectra of tridiagonal symmetric matrices” (2011). Here, we generalize those results to the ()-banded symmetric Toeplitz matrix operators for arbitrary positive integer .
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14

Wang, Hui, and Zhi Bin Li. "An Inverse Problem of Eigenvalue for Generalized Anti-Tridiagonal Matrices." Advanced Materials Research 424-425 (January 2012): 377–80. http://dx.doi.org/10.4028/www.scientific.net/amr.424-425.377.

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An inverse problem of eigenvalue for generalized Anti-Tridiagonal Matrices is discussed on the base of some inverse problems of Eigenvalue for Anti-Tridiagonal Matrices. The algorithm and uniqueness theorem of the solution of the problem are given, and some numerical example is provided
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15

Nomura, Kazumasa, and Paul Terwilliger. "Tridiagonal matrices with nonnegative entries." Linear Algebra and its Applications 434, no. 12 (June 2011): 2527–38. http://dx.doi.org/10.1016/j.laa.2011.01.003.

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16

Molinari, Luca Guido. "Determinants of block tridiagonal matrices." Linear Algebra and its Applications 429, no. 8-9 (October 2008): 2221–26. http://dx.doi.org/10.1016/j.laa.2008.06.015.

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17

Amodio, P., L. Brugnano, and T. Politi. "Parallel Factorizations for Tridiagonal Matrices." SIAM Journal on Numerical Analysis 30, no. 3 (June 1993): 813–23. http://dx.doi.org/10.1137/0730041.

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18

Al-Hassan, Qassem M. "On inverses of tridiagonal matrices." Journal of Discrete Mathematical Sciences and Cryptography 8, no. 1 (January 2005): 49–58. http://dx.doi.org/10.1080/09720529.2005.10698020.

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19

Diaconis, Persi, and Philip Matchett Wood. "Random doubly stochastic tridiagonal matrices." Random Structures & Algorithms 42, no. 4 (August 3, 2012): 403–37. http://dx.doi.org/10.1002/rsa.20452.

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20

Veerman, J. J. P., and David K. Hammond. "Tridiagonal Matrices and Boundary Conditions." SIAM Journal on Matrix Analysis and Applications 37, no. 1 (January 2016): 1–17. http://dx.doi.org/10.1137/140978909.

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21

Bohner, Martin, and Ondrej Doslý. "Positivity of Block Tridiagonal Matrices." SIAM Journal on Matrix Analysis and Applications 20, no. 1 (January 1998): 182–95. http://dx.doi.org/10.1137/s0895479897318794.

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22

Ikramov, Kh D. "On tridiagonal conjugate-normal matrices." Computational Mathematics and Mathematical Physics 47, no. 2 (February 2007): 173–79. http://dx.doi.org/10.1134/s0965542507020017.

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23

El-Mikkawy, Moawwad, and Abdelrahman Karawia. "Inversion of general tridiagonal matrices." Applied Mathematics Letters 19, no. 8 (August 2006): 712–20. http://dx.doi.org/10.1016/j.aml.2005.11.012.

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24

Brugnano, L., and D. Trigiante. "Tridiagonal matrices: Invertibility and conditioning." Linear Algebra and its Applications 166 (March 1992): 131–50. http://dx.doi.org/10.1016/0024-3795(92)90273-d.

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25

Rózsa, Pál, and Francesco Romani. "On periodic block-tridiagonal matrices." Linear Algebra and its Applications 167 (April 1992): 35–52. http://dx.doi.org/10.1016/0024-3795(92)90337-a.

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26

Sander, S. A. "A bound for tridiagonal matrices." Siberian Mathematical Journal 30, no. 4 (1990): 635–36. http://dx.doi.org/10.1007/bf00971763.

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27

Bebiano, Natália, and Susana Furtado. "Remarks on anti-tridiagonal matrices." Applied Mathematics and Computation 373 (May 2020): 125008. http://dx.doi.org/10.1016/j.amc.2019.125008.

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28

Dong, Chuan Dai. "A Fast Algorithm for the Inverse of a Class of Tridiagonal Period Matrices in Signal Processing." Advanced Materials Research 121-122 (June 2010): 204–8. http://dx.doi.org/10.4028/www.scientific.net/amr.121-122.204.

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The Tridiagonal period Matrices, as an important tool, have much important applications ( such as in computational mathematics, physics, image processing and recognition, missile system design, nonlinear kinetics, economics and biology etc). In this paper, we give a fast algorithm for the inverse of the class of tridiagonal period matrices .
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29

Dub, P., and O. Litzman. "The Darwin procedure in optics of layered media and the matrix theory." Acta Crystallographica Section A Foundations of Crystallography 55, no. 4 (July 1, 1999): 613–20. http://dx.doi.org/10.1107/s010876739801513x.

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The Darwin dynamical theory of diffraction for two beams yields a nonhomogeneous system of linear algebraic equations with a tridiagonal matrix. It is shown that different formulae of the two-beam Darwin theory can be obtained by a uniform view of the basic properties of tridiagonal matrices, their determinants (continuants) and their close relationship to continued fractions and difference equations. Some remarks concerning the relation of the Darwin theory in the three-beam case to tridiagonal block matrices are also presented.
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30

Xu, Wei-Ru, and Guo-Liang Chen. "On inverse eigenvalue problems for two kinds of special banded matrices." Filomat 31, no. 2 (2017): 371–85. http://dx.doi.org/10.2298/fil1702371x.

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This paper presents two kinds of symmetric tridiagonal plus paw form (hereafter TPPF) matrices, which are the combination of tridiagonal matrices and bordered diagonal matrices. In particular, we exploit the interlacing properties of their eigenvalues. On this basis, the inverse eigenvalue problems for the two kinds of symmetric TPPF matrices are to construct these matrices from the minimal and the maximal eigenvalues of all their leading principal submatrices respectively. The necessary and sufficient conditions for the solvability of the problems are derived. Finally, numerical algorithms and some examples of the results developed here are given.
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31

Vandebril, Raf. "On tridiagonal matrices unitarily equivalent to normal matrices." Linear Algebra and its Applications 432, no. 12 (July 2010): 3079–99. http://dx.doi.org/10.1016/j.laa.2010.02.009.

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32

Ikramov, Kh D. "Nonsymmetric Toeplitz matrices that commute with tridiagonal matrices." Mathematical Notes 55, no. 5 (May 1994): 483–90. http://dx.doi.org/10.1007/bf02110375.

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33

MOGHADDAMFAR, A. R., S. M. H. POOYA, S. NAVID SALEHY, and S. NIMA SALEHY. "FIBONACCI AND LUCAS SEQUENCES AS THE PRINCIPAL MINORS OF SOME INFINITE MATRICES." Journal of Algebra and Its Applications 08, no. 06 (December 2009): 869–83. http://dx.doi.org/10.1142/s0219498809003734.

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In the literature one may encounter certain infinite tridiagonal matrices, the principal minors of which, constitute the Fibonacci or Lucas sequence. The major purpose of this article is to find new infinite matrices with this property. It is interesting to mention that the matrices found are not tridiagonal which have been investigated before. Furthermore, we introduce the sequences composed of Fibonacci and Lucas k-numbers for the positive integer k and we construct the infinite matrices the principal minors of which generate these sequences.
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34

Kovačec, Alexander. "Schrödinger’s tridiagonal matrix." Special Matrices 9, no. 1 (January 1, 2021): 149–65. http://dx.doi.org/10.1515/spma-2020-0124.

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Abstract In the third part of his famous 1926 paper ‘Quantisierung als Eigenwertproblem’, Schrödinger came across a certain parametrized family of tridiagonal matrices whose eigenvalues he conjectured. A 1991 paper wrongly suggested that his conjecture is a direct consequence of an 1854 result put forth by Sylvester. Here we recount some of the arguments that led Schrödinger to consider this particular matrix and what might have led to the wrong suggestion. We then give a self-contained elementary (though computational) proof which would have been accessible to Schrödinger. It needs only partial fraction decomposition. We conclude this paper by giving an outline of the connection established in recent decades between orthogonal polynomial systems of the Hahn class and certain tridiagonal matrices with fractional entries. It also allows to prove Schrödinger’s conjecture.
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35

Bebiano, Natália, Providência da, Ilya Spitkovsky, and Kenya Vazquez. "Kippenhahn curves of some tridiagonal matrices." Filomat 35, no. 9 (2021): 3047–61. http://dx.doi.org/10.2298/fil2109047b.

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Tridiagonal matrices with constant main diagonal and reciprocal pairs of off-diagonal entries are considered. Conditions for such matrices with sizes up to 6-by-6 to have elliptical numerical ranges are obtained.
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36

da Fonseca, Carlos M., Victor Kowalenko, and László Losonczi. "Ninety years of k-tridiagonal matrices." Studia Scientiarum Mathematicarum Hungarica 57, no. 3 (October 20, 2020): 298–311. http://dx.doi.org/10.1556/012.2020.57.3.1466.

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AbstractThis survey revisits Jenő Egerváry and Otto Szász’s article of 1928 on trigonometric polynomials and simple structured matrices focussing mainly on the latter topic. In particular, we concentrate on the spectral theory for the first type of the matrices introduced in the article, which are today referred to as k-tridiagonal matrices, and then discuss the explosion of interest in them over the last two decades, most of which could have benefitted from the seminal article, had it not been overlooked.
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37

Altun, Muhammed. "Fine Spectra of Tridiagonal Symmetric Matrices." International Journal of Mathematics and Mathematical Sciences 2011 (2011): 1–10. http://dx.doi.org/10.1155/2011/161209.

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The fine spectra of upper and lower triangular banded matrices were examined by several authors. Here we determine the fine spectra of tridiagonal symmetric infinite matrices and also give the explicit form of the resolvent operator for the sequence spaces , , , and .
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38

Fonseca, Carlos M. da. "On some conjectures regarding tridiagonal matrices." Journal of Applied Mathematics and Computational Mechanics 17, no. 4 (December 2018): 13–17. http://dx.doi.org/10.17512/jamcm.2018.4.02.

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39

Ayzenberg, Anton. "Space of isospectral periodic tridiagonal matrices." Algebraic & Geometric Topology 20, no. 6 (December 8, 2020): 2957–94. http://dx.doi.org/10.2140/agt.2020.20.2957.

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40

Álvarez-Nodarse, R., J. Petronilho, and N. R. Quintero. "Spectral properties of certain tridiagonal matrices." Linear Algebra and its Applications 436, no. 3 (February 2012): 682–98. http://dx.doi.org/10.1016/j.laa.2011.07.040.

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41

Veerman, J. J. P., David K. Hammond, and Pablo E. Baldivieso. "Spectra of certain large tridiagonal matrices." Linear Algebra and its Applications 548 (July 2018): 123–47. http://dx.doi.org/10.1016/j.laa.2018.03.005.

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42

da Fonseca, C. M., and J. Petronilho. "Explicit inverses of some tridiagonal matrices." Linear Algebra and its Applications 325, no. 1-3 (March 2001): 7–21. http://dx.doi.org/10.1016/s0024-3795(00)00289-5.

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43

Dhillon, I. S., and A. N. Malyshev. "Inner deflation for symmetric tridiagonal matrices." Linear Algebra and its Applications 358, no. 1-3 (January 2003): 139–44. http://dx.doi.org/10.1016/s0024-3795(01)00479-7.

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44

Kulkarni, Devadatta, Darrell Schmidt, and Sze-Kai Tsui. "Eigenvalues of tridiagonal pseudo-Toeplitz matrices." Linear Algebra and its Applications 297, no. 1-3 (August 1999): 63–80. http://dx.doi.org/10.1016/s0024-3795(99)00114-7.

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45

Bultheel, A., P. González-Vera, E. Hendriksen, and O. Njåstad. "Orthogonal rational functions and tridiagonal matrices." Journal of Computational and Applied Mathematics 153, no. 1-2 (April 2003): 89–97. http://dx.doi.org/10.1016/s0377-0427(02)00602-7.

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46

Huang, Jie, Ronald D. Haynes, and Ting-Zhu Huang. "Monotonicity of Perturbed Tridiagonal $M$-Matrices." SIAM Journal on Matrix Analysis and Applications 33, no. 2 (January 2012): 681–700. http://dx.doi.org/10.1137/100812483.

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47

Commercon, J. C. "Eigenvalues of tridiagonal symmetric interval matrices." IEEE Transactions on Automatic Control 39, no. 2 (1994): 377–79. http://dx.doi.org/10.1109/9.272338.

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48

Özkoç, Arzu. "Tridiagonal Matrices via k-Balancing Number." British Journal of Mathematics & Computer Science 10, no. 4 (January 10, 2015): 1–11. http://dx.doi.org/10.9734/bjmcs/2015/19014.

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49

Łosiak, Janina, E. Neuman, and Jolanta Nowak. "The inversion of cyclic tridiagonal matrices." Applicationes Mathematicae 20, no. 1 (1988): 93–102. http://dx.doi.org/10.4064/am-20-1-93-102.

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50

Dubeau, F., and J. Savoie. "A remark on cyclic tridiagonal matrices." Applicationes Mathematicae 21, no. 2 (1991): 253–56. http://dx.doi.org/10.4064/am-21-2-253-256.

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