Tridiagonal matrix (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Tridiagonal matrix" in English language version.

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Thomas Muir (1960). A treatise on the theory of determinants. Dover Publications. pp. 516–525.

archives-ouvertes.fr

hal.archives-ouvertes.fr

This can also be written as $a+2{\sqrt {bc}}\cos(k\pi /{(n+1)})$ because $\cos(x)=-\cos(\pi -x)$ , as is done in: Kulkarni, D.; Schmidt, D.; Tsui, S. K. (1999). "Eigenvalues of tridiagonal pseudo-Toeplitz matrices" (PDF). Linear Algebra and Its Applications. 297 (1–3): 63–80. doi:10.1016/S0024-3795(99)00114-7.

arxiv.org

Bossu, Sebastien (2024). "Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices". Linear Algebra and Its Applications. 699: 129–158. arXiv:2304.06100. doi:10.1016/j.laa.2024.06.018.

doi.org

El-Mikkawy, M. E. A. (2004). "On the inverse of a general tridiagonal matrix". Applied Mathematics and Computation. 150 (3): 669–679. doi:10.1016/S0096-3003(03)00298-4.
Da Fonseca, C. M. (2007). "On the eigenvalues of some tridiagonal matrices". Journal of Computational and Applied Mathematics. 200: 283–286. doi:10.1016/j.cam.2005.08.047.
Usmani, R. A. (1994). "Inversion of a tridiagonal jacobi matrix". Linear Algebra and Its Applications. 212–213: 413–414. doi:10.1016/0024-3795(94)90414-6.
Hu, G. Y.; O'Connell, R. F. (1996). "Analytical inversion of symmetric tridiagonal matrices". Journal of Physics A: Mathematical and General. 29 (7): 1511. Bibcode:1996JPhA...29.1511H. doi:10.1088/0305-4470/29/7/020.
Huang, Y.; McColl, W. F. (1997). "Analytical inversion of general tridiagonal matrices". Journal of Physics A: Mathematical and General. 30 (22): 7919. Bibcode:1997JPhA...30.7919H. doi:10.1088/0305-4470/30/22/026.
Mallik, R. K. (2001). "The inverse of a tridiagonal matrix". Linear Algebra and Its Applications. 325 (1–3): 109–139. doi:10.1016/S0024-3795(00)00262-7.
Kılıç, E. (2008). "Explicit formula for the inverse of a tridiagonal matrix by backward continued fractions". Applied Mathematics and Computation. 197: 345–357. doi:10.1016/j.amc.2007.07.046.
Meurant, Gerard (1992). "A review on the inverse of symmetric tridiagonal and block tridiagonal matrices". SIAM Journal on Matrix Analysis and Applications. 13 (3): 707–728. doi:10.1137/0613045.
Bossu, Sebastien (2024). "Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices". Linear Algebra and Its Applications. 699: 129–158. arXiv:2304.06100. doi:10.1016/j.laa.2024.06.018.
Noschese, S.; Pasquini, L.; Reichel, L. (2013). "Tridiagonal Toeplitz matrices: Properties and novel applications". Numerical Linear Algebra with Applications. 20 (2): 302. doi:10.1002/nla.1811.
This can also be written as $a+2{\sqrt {bc}}\cos(k\pi /{(n+1)})$ because $\cos(x)=-\cos(\pi -x)$ , as is done in: Kulkarni, D.; Schmidt, D.; Tsui, S. K. (1999). "Eigenvalues of tridiagonal pseudo-Toeplitz matrices" (PDF). Linear Algebra and Its Applications. 297 (1–3): 63–80. doi:10.1016/S0024-3795(99)00114-7.
Coakley, E.S.; Rokhlin, V. (2012). "A fast divide-and-conquer algorithm for computing the spectra of real symmetric tridiagonal matrices". Applied and Computational Harmonic Analysis. 34 (3): 379–414. doi:10.1016/j.acha.2012.06.003.
Kreer, M. (1994). "Analytic birth-death processes: a Hilbert space approach". Stochastic Processes and Their Applications. 49 (1): 65–74. doi:10.1016/0304-4149(94)90112-0.
Eidelman, Yuli; Gohberg, Israel; Gemignani, Luca (2007-01-01). "On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms". Linear Algebra and Its Applications. 420 (1): 86–101. doi:10.1016/j.laa.2006.06.028. ISSN 0024-3795.

elsevier.com

authors.elsevier.com

Bossu, Sebastien (2024). "Tridiagonal and single-pair matrices and the inverse sum of two single-pair matrices". Linear Algebra and Its Applications. 699: 129–158. arXiv:2304.06100. doi:10.1016/j.laa.2024.06.018.

harvard.edu

ui.adsabs.harvard.edu

Hu, G. Y.; O'Connell, R. F. (1996). "Analytical inversion of symmetric tridiagonal matrices". Journal of Physics A: Mathematical and General. 29 (7): 1511. Bibcode:1996JPhA...29.1511H. doi:10.1088/0305-4470/29/7/020.
Huang, Y.; McColl, W. F. (1997). "Analytical inversion of general tridiagonal matrices". Journal of Physics A: Mathematical and General. 30 (22): 7919. Bibcode:1997JPhA...30.7919H. doi:10.1088/0305-4470/30/22/026.

hkbu.edu.hk

math.hkbu.edu.hk

Meurant, Gérard (October 2008). "Tridiagonal matrices" (PDF) – via Institute for Computational Mathematics, Hong Kong Baptist University.

utexas.edu

cs.utexas.edu

Dhillon, Inderjit Singh (1997). A New O(n²) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem (PDF) (PhD). University of California, Berkeley. p. 8. CSD-97-971, ADA637073.

worldcat.org

search.worldcat.org

Parlett, B.N. (1997) [1980]. The Symmetric Eigenvalue Problem. Classics in applied mathematics. Vol. 20. SIAM. ISBN 0-89871-402-8. OCLC 228147822.
Eidelman, Yuli; Gohberg, Israel; Gemignani, Luca (2007-01-01). "On the fast reduction of a quasiseparable matrix to Hessenberg and tridiagonal forms". Linear Algebra and Its Applications. 420 (1): 86–101. doi:10.1016/j.laa.2006.06.028. ISSN 0024-3795.