Relevant bibliographies by topics / Tridiagonal matrices

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Tridiagonal matrices'

Author: Grafiati
Published: 10 September 2021
Last updated: 25 April 2022

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Journal articles on the topic "Tridiagonal matrices"

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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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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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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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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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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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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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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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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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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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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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Dissertations / Theses on the topic "Tridiagonal matrices"

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Huang, Yuguang. "Algorithm design for structured matrix computations." Thesis, University of Oxford, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.325925.

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Stewart, James A. "The numerical solution of systems of equations with tridiagonal coefficient matrices." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape7/PQDD_0004/MQ46277.pdf.

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Ziad, Abderrahmane. "Contributions au calcul numérique des valeurs propres des matrices normales." Saint-Etienne, 1996. http://www.theses.fr/1996STET4001.

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Première partie: la convergence globale de l'algorithme QR avec le shift de Rayleigh appliquée à une matrice normale Hessenberg supérieure irréductible est démontrée. Ensuite nous avons proposé un shift avec lequel la convergence est cubique, lorsque la matrice est symétrique tridiagonale irréductible. Deuxième partie: nous avons proposé une méthode pour le calcul d'une valeur propre de rang donné d'une matrice symétrique tridiagonale irréductible, cette méthode est un procédé d'initialisation de la méthode dite d'itération inverse de Rayleigh
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Archid, Atika. "Méthodes par blocs adaptées aux matrices structurées et au calcul du pseudo-inverse." Thesis, Littoral, 2013. http://www.theses.fr/2013DUNK0394/document.

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Nous nous intéressons dans cette thèse, à l'étude de certaines méthodes numériques de type krylov dans le cas symplectique, en utilisant la technique de blocs. Ces méthodes, contrairement aux méthodes classiques, permettent à la matrice réduite de conserver la structure Hamiltonienne ou anti-Hamiltonienne ou encore symplectique d'une matrice donnée. Parmi ces méthodes, nous nous sommes intéressés à la méthodes d'Arnoldi symplectique par bloc que nous appelons aussi bloc J-Arnoldi. Notre but essentiel est d’étudier cette méthode de façon théorique et numérique, sur la nouvelle structure du K-module libre ℝ²nx²s avec K = ℝ²sx²s où s ≪ n désigne la taille des blocs utilisés. Un deuxième objectif est de chercher une approximation de l'epérateur exp(A)V, nous étudions en particulier le cas où A est une matrice réelle Hamiltonnienne et anti-symétrique de taille 2n x 2n et V est une matrice rectangulaire ortho-symplectique de taille 2n x 2s sur le sous-espace de Krylov par blocs Km(A,V) = blockspan {V,AV,...,Am-1V}, en conservant la structure de la matrice V. Cette approximation permet de résoudre plusieurs problèmes issus des équations différentielles dépendants d'un paramètre (EDP) et des systèmes d'équations différentielles ordinaires (EDO). Nous présentons également une méthode de Lanczos symplectique par bloc, que nous nommons bloc J-Lanczos. Cette méthode permet de réduire une matrice structurée sous la forme J-tridiagonale par bloc. Nous proposons des algorithmes basés sur deux types de normalisation : la factorisation S R et la factorisation Rj R. Dans une dernière partie, nous proposons un algorithme qui généralise la méthode de Greville afin de déterminer la pseudo inverse de Moore-Penros bloc de lignes par bloc de lignes d'une matrice rectangulaire de manière itérative. Nous proposons un algorithme qui utilise la technique de bloc. Pour toutes ces méthodes, nous proposons des exemples numériques qui montrent l'efficacité de nos approches
We study, in this thesis, some numerical block Krylov subspace methods. These methods preserve geometric properties of the reduced matrix (Hamiltonian or skew-Hamiltonian or symplectic). Among these methods, we interest on block symplectic Arnoldi, namely block J-Arnoldi algorithm. Our main goal is to study this method, theoretically and numerically, on using ℝ²nx²s as free module on (ℝ²sx²s, +, x) with s ≪ n the size of block. A second aim is to study the approximation of exp (A)V, where A is a real Hamiltonian and skew-symmetric matrix of size 2n x 2n and V a rectangular matrix of size 2n x 2s on block Krylov subspace Km (A, V) = blockspan {V, AV,...Am-1V}, that preserve the structure of the initial matrix. this approximation is required in many applications. For example, this approximation is important for solving systems of ordinary differential equations (ODEs) or time-dependant partial differential equations (PDEs). We also present a block symplectic structure preserving Lanczos method, namely block J-Lanczos algorithm. Our approach is based on a block J-tridiagonalization procedure of a structured matrix. We propose algorithms based on two normalization methods : the SR factorization and the Rj R factorization. In the last part, we proposea generalized algorithm of Greville method for iteratively computing the Moore-Penrose inverse of a rectangular real matrix. our purpose is to give a block version of Greville's method. All methods are completed by many numerical examples
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WAHA, NDEUNA LAURE. "Proprietes des matrices hamiltoniennes dans la base tridiagonale." Université Louis Pasteur (Strasbourg) (1971-2008), 1999. http://www.theses.fr/1999STR13065.

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Nous analysons le spectre d'une matrice defini par un hamiltonien h a (1+2) corps, agissant dans un espace de n particules. D'abord, il est demontre que la densite de niveaux est donnee par une fonction binomiale continue determinee par les trois premiers moments de h et par la dimension de l'espace. Les seules deviations apparaissent sur la position de l'etat fondamental du systeme. Pour le localiser, la theorie est reformulee en termes de l'algorithme de lanczos, dans lequel la base est definie en agissant de facon repetee sur un vecteur initial (|0>) et en orthogonalisant a chaque etape, ce qui nous conduit a la forme tridiagonale de la matrice. Il a ete demontre qu'avec un choix judicieux de |0>, les quelques premiers moments <0|h k|> sont suffisants pour determiner de facon precise l'energie de l'etat fondamental. Nous demontrons aussi que les elements de matrice (au dela des premiers n = o(n)) ont une forme generale-binomiale inverse pour les non-diagonaux, logarithme pour les diagonaux-entierement determinee par les memes quatre parametres definissant la densite de niveaux globale. Ces resultats sont utilises pour estimer la densite de niveaux en termes des fonctions de structure gamow teller experimentales.
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Larriba, Pey Josep Lluís. "Design and evaluation of tridiagonal solvers for vector and parallel computers." Doctoral thesis, Universitat Politècnica de Catalunya, 1995. http://hdl.handle.net/10803/6012.

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Rocha, Lindomar José. "Determinação de autovalores e autovetores de matrizes tridiagonais simétricas usando CUDA." reponame:Repositório Institucional da UnB, 2015. http://repositorio.unb.br/handle/10482/19625.

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Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.
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Diversos ramos do conhecimento humano fazem uso de autovalores e autovetores, dentre eles têm-se Física, Engenharia, Economia, etc. A determinação desses autovalores e autovetores pode ser feita utilizando diversas rotinas computacionais, porém umas mais rápidas que outras nesse senário de ganho de velocidade aparece a opção de se usar a computação paralela de forma mais especifica a CUDA da Nvidia é uma opção que oferece um ganho de velocidade significativo, nesse modelo as rotinas são executadas na GPU onde se tem diversos núcleos de processamento. Dada a tamanha importância dos autovalores e autovetores o objetivo desse trabalho é determinar rotinas que possam efetuar o cálculos dos mesmos com matrizes tridiagonais simétricas reais de maneira mais rápida e segura, através de computação paralela com uso da CUDA. Objetivo esse alcançado através da combinação de alguns métodos numéricos para a obtenção dos autovalores e um alteração no método da iteração inversa utilizado na determinação dos autovetores. Temos feito uso de rotinas LAPACK para comparar com as nossas rotinas desenvolvidas em CUDA. De acordo com os resultados, a rotina desenvolvida em CUDA tem a vantagem clara de velocidade quer na precisão simples ou dupla, quando comparado com o estado da arte das rotinas de CPU a partir da biblioteca LAPACK. ______________________________________________________________________________________________ ABSTRACT
Severa branches of human knowledge make use of eigenvalues and eigenvectors, among them we have physics, engineering, economics, etc. The determination of these eigenvalues and eigenvectors can be using various computational routines, som faster than others in this speed increase scenario appears the option to use the parallel computing more specifically the Nvidia’s CUDA is an option that provides a gain of significant speed, this model the routines are performed on the GPU which has several processing cores. Given the great importance of the eigenvalues and eigenvectors the objective of this study is to determine routines that can perform the same calculations with real symmetric tridiagonal matrices more quickly and safely, through parallel computing with use of CUDA. Objective that achieved by some combination of numerical methods to obtain the eigenvalues and a change in the method of inverse iteration used to determine of the eigenvectors, which was used LAPACK routines to compare with routine developed in CUDA. According to the results of the routine developed in CUDA has marked superiority with single or double precision, in the question speed regarding the routines of LAPACK.
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Miranda, Wilson Domingos Sidinei Alves. "Algoritmo paralelo para determinação de autovalores de matrizes hermitianas." reponame:Repositório Institucional da UnB, 2015. http://repositorio.unb.br/handle/10482/20642.

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Dissertação (mestrado)–Universidade de Brasília, Universidade UnB de Planaltina, Programa de Pós-Graduação em Ciência de Materiais, 2015.
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Um dos principais problemas da álgebra linear computacional é o problema de autovalor, Au = lu, onde A é usualmente uma matriz de ordem grande. A maneira mais efetiva de resolver tal problema consiste em reduzir a matriz A para a forma tridiagonal e usar o método da bissecção ou algoritmo QR para encontrar alguns ou todos os autovalores. Este trabalho apresenta uma implementação em paralelo utilizando uma combinação dos métodos da bissecção, secante e Newton-Raphson para a solução de problemas de autovalores de matrizes hermitianas. A implementação é voltada para unidades de processamentos gráficos (GPUs) visando a utilização em computadores que possuam placas gráficas com arquitetura CUDA. Para comprovar a eficiência e aplicabilidade da implementação, comparamos o tempo gasto entre os algoritmos usando a GPU, a CPU e as rotinas DSTEBZ e DSTEVR da biblioteca LAPACK. O problema foi dividido em três fases, tridiagonalização, isolamento e extração, as duas últimas calculadas na GPU. A tridiagonalização via DSYTRD da LAPACK, calculada em CPU, mostrou-se mais eficiente do que a realizada em CUDA via DSYRDB. O uso do método zeroinNR na fase de extração em CUDA foi cerca de duas vezes mais rápido que o método da bissecção em CUDA. Então o método híbrido é o mais eficiente para o nosso caso. _______________________________________________________________________________________________ ABSTRACT
One of the main problems in computational linear algebra is the eigenvalue problem Au = lu, where A is usually a matrix of big order. The most effective way to solve this problem is to reduce the matrix A to tridiagonal form and use the method of bisection or QR algorithm to find some or all of the eigenvalues. This work presents a parallel implementation using a combination of methods bisection, secant and Newton-Raphson for solving the eigenvalues problem for Hermitian matrices. Implementation is focused on graphics processing units (GPUs) aimed at use in computers with graphics cards with CUDA architecture. To prove the efficiency and applicability of the implementation, we compare the time spent between the algorithms using the GPU, the CPU and DSTEBZ and DSTEVR routines from LAPACK library. The problem was divided into three phases, tridiagonalization, isolation and extraction, the last two calculated on the GPU. The tridiagonalization by LAPACK’s DSYTRD, calculated on the CPU, proved more efficient than the DSYRDB in CUDA. The use of the method zeroinNR on the extraction phase in CUDA was about two times faster than the bisection method in CUDA. So the hybrid method is more efficient for our case.
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Ceresoli, Eliamar. "O método de divisão-e-conquista na solução de auto-sistemas de matrizes simétricas." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2002. http://hdl.handle.net/10183/1642.

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O presente trabalho apresenta um estudo do método de divisão-e-conquista para solução dos auto-sistemas de matrizes tridiagonais simétricas. Inicialmente, explanamos a parte teórica, e posteriormente, por meio de exemplos numéricos mostramos seu funcionamento. Para a realização deste estudo, utilizou-se o software Maple como ferramenta auxiliar. Realizamos comparações e análises dos auto-sistemas encontrados com as rotinas DSTEDC e DSTEQR do LAPACK, que utilizam respectivamente o método de divisão-e-conquista e o método QR e também comparamos estes com os resultados encontrados por nós. Verificamos por meio de testes os tempos, que as rotinas citadas, dispendem na resolução de alguns auto-sistemas. Os resultados apresentados mostram que o método de Divisão-e-Conquista é competitivo com o método tradicional, QR, para o cálculo de autovalores e autovetores de matrizes tridiagonais simétricas.
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CHERN, JIANN JONG, and 陳建中. "Geometry of Tridiagonal Matrices." Thesis, 1995. http://ndltd.ncl.edu.tw/handle/43801829444561600253.

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碩士
國立中山大學
應用數學研究所
83
Tridiagonal Matrices are special square matrices. Their nonzero elements only occure at diagonals and subdiagonals. Other entries are zero. Such matrices play an important role in matrix theory and matrix computation. This paper consider such matrix as a function of its diagonal vector, that is, the subdiagonals are fixed constants. If we consider the set of all vectors such that the value of this function is a singular matrix, then this set will be the union of n disjoint surfaces in n dimensional space and each surface is a connected closed set. We will explore the geometric properties of these surfaces. Moreover, the set of all vectors such that the value of the function is a nonsingular matrix and the geometric meaning of eigenvalues will also be discussed in this paper.
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Books on the topic "Tridiagonal matrices"

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Sun, Xian-He. A fast parallel tridiagonal algorithm for a class of CFD applications. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1996.

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Gill, Doron. An O(N2) method for computing the Eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach. Hampton, Va: ICASE, 1988.

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Spectral analysis, differential equations, and mathematical physics: A festschrift in honor of Fritz Gesztesy's 60th birthday. Providence, Rhode Island: American Mathematical Society, 2013.

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An O(N) method for computing the eigensystem of N x N symmetric tridiagonal matrices by the divide and conquer approach. Hampton, Va: National Aeronautics and Space Administration, Langley Research Center, 1988.

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Book chapters on the topic "Tridiagonal matrices"

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Cullum, Jane K., and Ralph A. Willoughby. "Tridiagonal Matrices." In Lanczos Algorithms for Large Symmetric Eigenvalue Computations Vol. I Theory, 76–91. Boston, MA: Birkhäuser Boston, 1985. http://dx.doi.org/10.1007/978-1-4684-9190-6_4.

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Cheng, Sui-Sun. "Regular Domains of Tridiagonal Matrices." In Numerical Mathematics Singapore 1988, 105–13. Basel: Birkhäuser Basel, 1988. http://dx.doi.org/10.1007/978-3-0348-6303-2_9.

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Godunov, S. K., A. G. Antonov, O. P. Kiriljuk, and V. I. Kostin. "Sturm Sequences of Tridiagonal Matrices." In Guaranteed Accuracy in Numerical Linear Algebra, 313–423. Dordrecht: Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-011-1952-8_4.

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Lyche, Tom. "Diagonally Dominant Tridiagonal Matrices; Three Examples." In Numerical Linear Algebra and Matrix Factorizations, 27–55. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36468-7_2.

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Lyche, Tom, Georg Muntingh, and Øyvind Ryan. "Diagonally Dominant Tridiagonal Matrices; Three Examples." In Texts in Computational Science and Engineering, 17–33. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59789-4_2.

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Adam, Maria, and John Maroulas. "The Joint Numerical Range of Bordered and Tridiagonal Matrices." In Linear Operators and Matrices, 29–41. Basel: Birkhäuser Basel, 2002. http://dx.doi.org/10.1007/978-3-0348-8181-4_5.

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Mastronardi, Nicola, Harold Taeter, and Paul Van Dooren. "On Computing Eigenvectors of Symmetric Tridiagonal Matrices." In Structured Matrices in Numerical Linear Algebra, 181–95. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-04088-8_9.

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Spellacy, Louise, and Darach Golden. "Partial Inverses of Complex Block Tridiagonal Matrices." In Parallel Processing and Applied Mathematics, 634–45. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-78024-5_55.

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Barreras, Álvaro, and Juan Manuel Peña. "On Tridiagonal Sign Regular Matrices and Generalizations." In Advances in Differential Equations and Applications, 239–47. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06953-1_23.

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Tsuchiya, T., and Q. Fang. "An Explicit Inversion Formula for Tridiagonal Matrices." In Topics in Numerical Analysis, 227–38. Vienna: Springer Vienna, 2001. http://dx.doi.org/10.1007/978-3-7091-6217-0_17.

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Conference papers on the topic "Tridiagonal matrices"

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Coelho, Diego F. G., and Vassil S. Dimitrov. "Fast estimation of tridiagonal matrices largest eigenvalue." In 2017 IEEE 30th Canadian Conference on Electrical and Computer Engineering (CCECE). IEEE, 2017. http://dx.doi.org/10.1109/ccece.2017.7946693.

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Wang, Hui, and Zhi-bin Li. "The Inverse Eigenproblem for Anti-Tridiagonal Matrices." In 2011 Third Pacific-Asia Conference on Circuits, Communications and System (PACCS). IEEE, 2011. http://dx.doi.org/10.1109/paccs.2011.5990182.

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STRANG, GILBERT. "BLOCK TRIDIAGONAL MATRICES AND THE KALMAN FILTER." In Proceedings of the International Conference of Computational Harmonic Analysis. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812776679_0014.

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Spellacy, Louise, and Darach Golden. "Partial inverses of block tridiagonal non-Hermitian matrices." In 2016 International Conference on High Performance Computing & Simulation (HPCS). IEEE, 2016. http://dx.doi.org/10.1109/hpcsim.2016.7568450.

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Li, Zhibin, and Xinxin Zhao. "The Inverse Eigenvalue Problem for Tridiagonal Matrices With Linear Relation." In 2009 First International Conference on Information Science and Engineering. IEEE, 2009. http://dx.doi.org/10.1109/icise.2009.1225.

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Holzel, Matthew. "Tridiagonal companion matrices and their use for computing orthogonal and nonorthogonal polynomial zeros." In 2017 25th Mediterranean Conference on Control and Automation (MED). IEEE, 2017. http://dx.doi.org/10.1109/med.2017.7984145.

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Taskara, N., K. Uslu, Y. Yazlik, N. Yilmaz, Theodore E. Simos, George Psihoyios, Ch Tsitouras, and Zacharias Anastassi. "The Construction of Horadam Numbers in Terms of the Determinant of Tridiagonal Matrices." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2011: International Conference on Numerical Analysis and Applied Mathematics. AIP, 2011. http://dx.doi.org/10.1063/1.3636739.

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Luszczek, Piotr, Hatem Ltaief, and Jack Dongarra. "Two-Stage Tridiagonal Reduction for Dense Symmetric Matrices Using Tile Algorithms on Multicore Architectures." In Distributed Processing Symposium (IPDPS). IEEE, 2011. http://dx.doi.org/10.1109/ipdps.2011.91.

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García-Illescas, M. A., and Luis Alvarez-Icaza. "On-Line Identification of Three-Dimensional Shear Building Models." In ASME 2017 Dynamic Systems and Control Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/dscc2017-5102.

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Abstract:
An on-line identification scheme for shear building models using recursive least squares with a matrix parameterized model is presented. Based on Gershgorin circles and tridiagonal matrices properties, the identified model stability is guaranteed in the presence of low excitation or low damping. Stability of the model helps in the design of more robust control laws. The scheme is evaluated in an experimental test-bed with a scaled five stories building where an on-line reduced order model is derived. Results indicate that when employing this matrix parametrization, a significant reduction in the number of calculations involved is achieved, when compared to the standard vector parametrization based schemes, such that real-time applications are feasible to implement. Moreover, the stability on the identified model is preserved.
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Carrion, Marcelo, Lucia Catabriga, Alvaro Coutinho, William Batty, and Ehsan Naeini. "A Parallel Multigrid Solver For Block-Tridiagonal Stencil Matrices Derived From Acoustic Wave Equation On Large Finite Difference Grids." In CNMAC 2016 - XXXVI Congresso Nacional de Matemática Aplicada e Computacional. SBMAC, 2017. http://dx.doi.org/10.5540/03.2017.005.01.0098.

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