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Relevant bibliographies by topics / Matriz tridiagonal

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Academic literature on the topic 'Matriz tridiagonal'

Author: Grafiati

Published: 4 June 2021

Last updated: 15 February 2022

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Journal articles on the topic "Matriz tridiagonal"

1

Rasmawati, Rasmawati, Lailany Yahya, Agusyarif Rezka Nuha, and Resmawan Resmawan. "DETERMINAN SUATU MATRIKS TOEPLITZ K-TRIDIAGONAL MENGGUNAKAN METODE REDUKSI BARIS DAN EKSPANSI KOFAKTOR." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 9, no. 1 (2021): 6–16. http://dx.doi.org/10.34312/euler.v9i1.10354.

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This paper discusses the determinants of a k-tridiagonal Toeplitz matrix using row reduction and cofactor expansion methods. The analysis was carried out recursively from the general form of the determinant of the tridiagonal Toeplitz matrix, the determinant of the 2-tridiagonal Toeplitz matrix, and the determinant of the 3-tridiagonal Toeplitz matrix. In the end, the general form of the determinant of the k-tridiagonal Toeplitz matrix is obtained.

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2

Kovačec, Alexander. "Schrödinger’s tridiagonal matrix." Special Matrices 9, no. 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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3

Zgirouski, A. A., and N. A. Likhoded. "Modified method of parallel matrix sweep." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 4 (2020): 425–34. http://dx.doi.org/10.29235/1561-2430-2019-55-4-425-434.

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The topic of this paper refers to efficient parallel solvers of block-tridiagonal linear systems of equations. Such systems occur in numerous modeling problems and require usage of high-performance multicore computation systems. One of the widely used methods for solving block-tridiagonal linear systems in parallel is the original block-tridiagonal sweep method. We consider the algorithm based on the partitioning idea. Firstly, the initial matrix is split into parts and transformations are applied to each part independently to obtain equations of a reduced block-tridiagonal system. Secondly, the reduced system is solved sequentially using the classic Thomas algorithm. Finally, all the parts are solved in parallel using the solutions of a reduced system. We propose a modification of this method. It was justified that if known stability conditions for the matrix sweep method are satisfied, then the proposed modification is stable as well.

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4

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 (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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5

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 (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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6

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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7

Nomura, Kazumasa, and Paul Terwilliger. "Totally bipartite tridiagonal pairs." Electronic Journal of Linear Algebra 37 (June 22, 2021): 434–91. http://dx.doi.org/10.13001/ela.2021.5029.

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There is a concept in linear algebra called a tridiagonal pair. The concept was motivated by the theory of $Q$-polynomial distance-regular graphs. We give a tutorial introduction to tridiagonal pairs, working with a special case as a concrete example. The special case is called totally bipartite, or totally bipartite (TB). Starting from first principles, we give an elementary but comprehensive account of TB tridiagonal pairs. The following topics are discussed: (i) the notion of a TB tridiagonal system; (ii) the eigenvalue array; (iii) the standard basis and matrix representations; (iv) the intersection numbers; (v) the Askey--Wilson relations; (vi) a recurrence involving the eigenvalue array; (vii) the classification of TB tridiagonal systems; (viii) self-dual TB tridiagonal pairs and systems; (ix) the $\mathbb{Z}_3$-symmetric Askey--Wilson relations; (x) some automorphisms and antiautomorphisms associated with a TB tridiagonal pair; and (xi) an action of the modular group ${\rm PSL}_2(\mathbb{Z})$ associated with a TB tridiagonal pair.

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8

Qi, Feng, and Ai-Qi Liu. "Alternative proofs of some formulas for two tridiagonal determinants." Acta Universitatis Sapientiae, Mathematica 10, no. 2 (2018): 287–97. http://dx.doi.org/10.2478/ausm-2018-0022.

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Abstract In the paper, the authors provide five alternative proofs of two formulas for a tridiagonal determinant, supply a detailed proof of the inverse of the corresponding tridiagonal matrix, and provide a proof for a formula of another tridiagonal determinant. This is a companion of the paper [F. Qi, V. Čerňanová,and Y. S. Semenov, Some tridiagonal determinants related to central Delannoy numbers, the Chebyshev polynomials, and the Fibonacci polynomials, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 81 (2019), in press.

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9

Chen, Kwang-Wu. "Horadam Sequences and Tridiagonal Determinants." Symmetry 12, no. 12 (2020): 1968. http://dx.doi.org/10.3390/sym12121968.

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We consider a family of particular tridiagonal matrix determinants which can represent the general second-order linear recurrence sequences. These determinants can be changed to symmetric or skew-symmetric tridiagonal determinants. To evaluate the complex factorizations of any Horadam sequence, we evaluate the eigenvalues of some special tridiagonal matrices and their corresponding eigenvectors. We also use these determinant representations to obtain some formulas in these sequences.

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10

Usmani, R. A. "Inversion of Jacobi's tridiagonal matrix." Computers & Mathematics with Applications 27, no. 8 (1994): 59–66. http://dx.doi.org/10.1016/0898-1221(94)90066-3.

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