Relevant bibliographies by topics / Factorization of matrices

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

Academic literature on the topic 'Factorization of matrices'

Author: Grafiati
Published: 4 June 2021
Last updated: 10 February 2022

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Journal articles on the topic "Factorization of matrices"

1

Liu, Jinwang, Tao Wu, Dongmei Li, and Jiancheng Guan. "On Zero Left Prime Factorizations for Matrices over Unique Factorization Domains." Mathematical Problems in Engineering 2020 (April 22, 2020): 1–3. http://dx.doi.org/10.1155/2020/1684893.

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In this paper, zero prime factorizations for matrices over a unique factorization domain are studied. We prove that zero prime factorizations for a class of matrices exist. Also, we give an algorithm to directly compute zero left prime factorizations for this class of matrices.
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Ng, Wei Shean, and Wei Wen Tan. "Some properties of various types of matrix factorization." ITM Web of Conferences 36 (2021): 03003. http://dx.doi.org/10.1051/itmconf/20213603003.

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Matrix factorizations or matrix decompositions are methods that represent a matrix as a product of two or more matrices. There are various types of matrix factorizations such as LU factorization, Cholesky factorization, singular value decomposition etc. Matrix factorization is widely used in pattern recognition, image denoising, data clustering etc. Motivated by these applications, some properties and applications of various types of matrix factorizations are studied. One of the purposes of matrix factorization is to ease the computation. Thus, comparisons in term of computation time of variou
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Chen, Yi-Zhi. "On Factorizations of Upper Triangular Nonnegative Matrices of Order Three." Discrete Dynamics in Nature and Society 2015 (2015): 1–6. http://dx.doi.org/10.1155/2015/960182.

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LetT3(N0)denote the semigroup of3×3upper triangular matrices with nonnegative integral-valued entries. In this paper, we investigate factorizations of upper triangular nonnegative matrices of order three. Firstly, we characterize the atoms of the subsemigroupSof the matrices inT3(N0)with nonzero determinant and give some formulas. As a consequence, problems 4a and 4c presented by Baeth et al. (2011) are each half-answered for the casen=3. And then, we consider some factorization cases of matrixAinSwithρ(A)=1and give formulas for the minimum factorization length of some special matrices inS.
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Qian, Guoyou, and Jingya Lu. "LU-FACTORIZATIONS OF SYMMETRIC MATRICES WITH APPLICATIONS." Asian-European Journal of Mathematics 03, no. 01 (2010): 133–43. http://dx.doi.org/10.1142/s179355711000009x.

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In this paper, we describe explicitly the LU -factorization of a symmetric matrix of order n with n ≤ 7 when each of its ordered principal minors is nonzero. By using this result and some other related results on non-singularity previously given by Smith, Beslin, Hong, Lee and Ligh in the literature, we establish several theorems concerning LU -factorizations of power GCD matrices, power LCM matrices and reciprocal power GCD matrices and reciprocal power LCM matrices.
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Eto, Kazufumi. "ON ROW-FACTORIZATION MATRICES." Journal of Algebra, Number Theory: Advances and Applications 17, no. 2 (2017): 93–108. http://dx.doi.org/10.18642/jantaa_7100121851.

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Maroulas, John. "Factorization of Hessenberg matrices." Linear Algebra and its Applications 506 (October 2016): 226–43. http://dx.doi.org/10.1016/j.laa.2016.05.026.

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Botha, J. D. "Idempotent factorization of matrices." Linear and Multilinear Algebra 40, no. 4 (1996): 365–71. http://dx.doi.org/10.1080/03081089608818452.

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Sourour, A. R. "Nilpotent factorization of matrices." Linear and Multilinear Algebra 31, no. 1-4 (1992): 303–8. http://dx.doi.org/10.1080/03081089208818141.

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Dita, P. "Factorization of unitary matrices." Journal of Physics A: Mathematical and General 36, no. 11 (2003): 2781–89. http://dx.doi.org/10.1088/0305-4470/36/11/309.

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Sourour, A. R., and Kunikyo Tang. "Factorization of singular matrices." Proceedings of the American Mathematical Society 116, no. 3 (1992): 629. http://dx.doi.org/10.1090/s0002-9939-1992-1097352-4.

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Dissertations / Theses on the topic "Factorization of matrices"

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Johnson, Paul D. "Factorization of Quasiseparable Matrices." Digital Archive @ GSU, 2008. http://digitalarchive.gsu.edu/math_theses/65.

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This paper investigates some of the ideas and algorithms developed for exploiting the structure of quasiseparable matrices. The case of purely scalar generators is considered initially. The process by which a quasiseparable matrix is represented as the product of matrices comprised of its generators is explained. This is done clearly in the scalar case, but may be extended to block generators. The complete factoring approach is then considered. This consists of two stages: inner-outer factorization followed by inner-coprime factorization. Finally, the stability of the algorithm is invest
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THIYAGARAJAN, SANJEEV. "REDUCING MEMORY SPACE FOR COMPLETELY UNROLLED LU FACTORIZATION OF SPARSE MATRICES." University of Cincinnati / OhioLINK, 2001. http://rave.ohiolink.edu/etdc/view?acc_num=ucin990556295.

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Zhu, Fei. "Kernel nonnegative matrix factorization : application to hyperspectral imagery." Thesis, Troyes, 2016. http://www.theses.fr/2016TROY0024/document.

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Cette thèse vise à proposer de nouveaux modèles pour la séparation de sources dans le cadre non linéaire des méthodes à noyaux en apprentissage statistique, et à développer des algorithmes associés. Le domaine d'application privilégié est le démélange en imagerie hyperspectrale. Tout d'abord, nous décrivons un modèle original de la factorisation en matrices non négatives (NMF), en se basant sur les méthodes à noyaux. Le modèle proposé surmonte la malédiction de préimage, un problème inverse hérité des méthodes à noyaux. Dans le même cadre proposé, plusieurs extensions sont développées pour int
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Xue, Yun. "Non-negative matrix factorization for face recognition." HKBU Institutional Repository, 2007. http://repository.hkbu.edu.hk/etd_ra/815.

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Syed, Akber. "A Hardware Interpreter for Sparse Matrix LU Factorization." University of Cincinnati / OhioLINK, 2002. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1024934521.

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Arslan, Bahar. "Functions of structured matrices." Thesis, University of Manchester, 2017. https://www.research.manchester.ac.uk/portal/en/theses/functions-of-structured-matrices(75511801-f8b8-4ac3-9434-35f88b1d0bb0).html.

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The growing interest in computing structured matrix functions stems from the fact that preserving and exploiting the structure of matrices can help us gain physically meaningful solutions with less computational cost and memory requirement. The work presented here is divided into two parts. The first part deals with the computation of functions of structured matrices. The second part is concerned with the structured error analysis in the computation of matrix functions. We present algorithms applying the inverse scaling and squaring method and using the Schur-like form of the symplectic matric
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Dailey, Megan. "RELATIVE PERTURBATION THEORY FOR DIAGONALLY DOMINANT MATRICES." UKnowledge, 2013. http://uknowledge.uky.edu/math_etds/11.

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Diagonally dominant matrices arise in many applications. In this work, we exploit the structure of diagonally dominant matrices to provide sharp entrywise relative perturbation bounds. We first generalize the results of Dopico and Koev to provide relative perturbation bounds for the LDU factorization with a well conditioned L factor. We then establish relative perturbation bounds for the inverse that are entrywise and independent of the condition number. This allows us to also present relative perturbation bounds for the linear system Ax=b that are independent of the condition number. Lastly,
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Takahashi, Ryan. "Structured Matrices and the Algebra of Displacement Operators." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/hmc_theses/45.

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Matrix calculations underlie countless problems in science, mathematics, and engineering. When the involved matrices are highly structured, displacement operators can be used to accelerate fundamental operations such as matrix-vector multiplication. In this thesis, we provide an introduction to the theory of displacement operators and study the interplay between displacement and natural matrix constructions involving direct sums, Kronecker products, and blocking. We also investigate the algebraic behavior of displacement operators, developing results about invertibility and kernels.
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Wu, Min. "On solutions of linear functional systems and factorization of modules over Laurent-Ore algebras." Nice, 2005. http://www.theses.fr/2005NICE4026.

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Rigaud, François. "Modèles de signaux musicaux informés par la physiques des instruments : Application à l'analyse automatique de musique pour piano par factorisation en matrices non-négatives." Thesis, Paris, ENST, 2013. http://www.theses.fr/2013ENST0073/document.

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Cette thèse introduit des nouveaux modèles de signaux musicaux informés par la physique des instruments. Alors que les communautés de l'acoustique instrumentale et du traitement du signal considèrent la modélisation des sons instrumentaux suivant deux approches différentes (respectivement, une modélisation du mécanisme de production du son, opposée à une modélisation des caractéristiques "morphologiques" générales du son), cette thèse propose une approche collaborative en contraignant des modèles de signaux génériques à l'aide d'information basée sur l'acoustique. L'effort est ainsi porté sur
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Books on the topic "Factorization of matrices"

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Litvinchuk, G. S. Factorization of measurable matrix functions. Akademie-Verlag, 1987.

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1953-, Spitkovskiĭ Ilya M., and Heinig Georg, eds. Factorization of measurable matrix functions. Birkhäuser Verlag, 1987.

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Higham, Nicholas J. Functions of matrices: Theory and computation. Society for Industrial and Applied Mathematics, 2008.

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Jones, Mark T. Bunch-Kaufman factorization for real symmetric indefinite banded matrices. ICASE, 1989.

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Venugopal, Sesh. Effects of partitioning and scheduling sparse matrix factorization on communication and load balance. National Aeronautics and Space Administration, Langley Research Center, 1991.

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Rawlins, A. D. A note on polynomial diagonalization and Wiener-Hopf factorization of 2x2 matrices. Brunel University, Department of Mathematics and Statistics, 1989.

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Pan, Victor. A fast, preconditioned conjugate gradient Toeplitz solver. Research Institute for Advanced Computer Science, NASA Ames Research Center, 1989.

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Guattery, Stephen. Graph embedding techniques for bounding condition numbers of incomplete factor preconditioners. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1997.

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Solving linear systems: An analysis of matrix prefactorization iterative methods. Matrix Editions, 2009.

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George, Alan. An analysis of spectral envelope-reduction via quadratic assignment problems. Institute for Computer Applications in Science and Engineering, NASA Langley Research Center, 1994.

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Book chapters on the topic "Factorization of matrices"

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Gohberg, Israel, Marinus A. Kaashoek, and Frederik van Schagen. "Factorization of Operator Polynomials." In Partially Specified Matrices and Operators: Classification, Completion, Applications. Birkhäuser Basel, 1995. http://dx.doi.org/10.1007/978-3-0348-9100-4_14.

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Constantinescu, Tiberiu. "Schur Parameters and Positive Block Matrices." In Schur Parameters, Factorization and Dilation Problems. Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9108-0_1.

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Böttcher, Albrecht, and Sergei Grudsky. "Toeplitz Matrices with Slowly Growing Pseudospectra." In Factorization, Singular Operators and Related Problems. Springer Netherlands, 2003. http://dx.doi.org/10.1007/978-94-017-0227-0_4.

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Lyche, Tom. "LDL* Factorization and Positive Definite Matrices." In Numerical Linear Algebra and Matrix Factorizations. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-36468-7_4.

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Dym, Harry. "Triangular factorization and positive definite matrices." In Graduate Studies in Mathematics. American Mathematical Society, 2013. http://dx.doi.org/10.1090/gsm/078/12.

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Lev-Ari, Hanoch, and Thomas Kailath. "Triangular Factorization of Structured Hermitian Matrices." In I. Schur Methods in Operator Theory and Signal Processing. Birkhäuser Basel, 1986. http://dx.doi.org/10.1007/978-3-0348-5483-2_12.

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Lyche, Tom, Georg Muntingh, and Øyvind Ryan. "LDL* Factorization and Positive Definite Matrices." In Texts in Computational Science and Engineering. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-59789-4_4.

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D’Angelo, John P. "Holomorphic Factorization of Matrices of Polynomials." In Reproducing Kernels and their Applications. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4757-2987-0_2.

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Klotz, Gerhard. "Factorization of Matrices with Maximum Accuracy." In Hector. Springer Berlin Heidelberg, 1988. http://dx.doi.org/10.1007/978-3-642-73576-9_6.

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Eidelman, Yuli, Israel Gohberg, and Iulian Haimovici. "The LDU Factorization and Inversion." In Separable Type Representations of Matrices and Fast Algorithms. Springer Basel, 2013. http://dx.doi.org/10.1007/978-3-0348-0606-0_18.

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Conference papers on the topic "Factorization of matrices"

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Lemaitre, Florian, and Lionel Lacassagne. "Batched Cholesky factorization for tiny matrices." In 2016 Conference on Design and Architectures for Signal and Image Processing (DASIP). IEEE, 2016. http://dx.doi.org/10.1109/dasip.2016.7853809.

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Aguiar, Pedro M. Q., Joao M. F. Xavier, and Marko Stosic. "Spectrally optimal factorization of incomplete matrices." In 2008 IEEE Conference on Computer Vision and Pattern Recognition (CVPR). IEEE, 2008. http://dx.doi.org/10.1109/cvpr.2008.4587675.

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Sugimoto, Kenji, Michael Sebek, and Didier Henrion. "Polynomial matrices and recursive QR factorization." In 2001 European Control Conference (ECC). IEEE, 2001. http://dx.doi.org/10.23919/ecc.2001.7076506.

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Finta, Béla, George Maroulis, and Theodore E. Simos. "The QR Factorization for Infinite Matrices." In COMPUTATIONAL METHODS IN SCIENCE AND ENGINEERING: Advances in Computational Science: Lectures presented at the International Conference on Computational Methods in Sciences and Engineering 2008 (ICCMSE 2008). AIP, 2009. http://dx.doi.org/10.1063/1.3225427.

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Baranoski, E. J. "Triangular factorization of inverse data covariance matrices." In [Proceedings] ICASSP 91: 1991 International Conference on Acoustics, Speech, and Signal Processing. IEEE, 1991. http://dx.doi.org/10.1109/icassp.1991.150863.

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Adams, R. J., and J. C. Young. "A diagonal factorization for integral equation matrices." In 2016 International Conference on Electromagnetics in Advanced Applications (ICEAA). IEEE, 2016. http://dx.doi.org/10.1109/iceaa.2016.7731523.

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Kohjima, Masahiro, Tatsushi Matsubayashi, and Hiroshi Sawada. "Probabilistic Non-negative Inconsistent-resolution Matrices Factorization." In CIKM'15: 24th ACM International Conference on Information and Knowledge Management. ACM, 2015. http://dx.doi.org/10.1145/2806416.2806636.

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Gruninger, John. "Non-negative factorization of non-negative matrices." In Remote Sensing, edited by Lorenzo Bruzzone. SPIE, 2007. http://dx.doi.org/10.1117/12.738381.

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George, Thomas, Vaibhav Saxena, Anshul Gupta, Amik Singh, and Anamitra R. Choudhury. "Multifrontal Factorization of Sparse SPD Matrices on GPUs." In Distributed Processing Symposium (IPDPS). IEEE, 2011. http://dx.doi.org/10.1109/ipdps.2011.44.

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Vouras, Peter G., and Trac D. Tran. "Factorization of paraunitary polyphase matrices using subspace projections." In 2008 42nd Asilomar Conference on Signals, Systems and Computers. IEEE, 2008. http://dx.doi.org/10.1109/acssc.2008.5074476.

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Reports on the topic "Factorization of matrices"

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Reif, John H. O(log2 n) Time Efficient Parallel Factorization of Dense, Sparse Separable, and Banded Matrices. Defense Technical Information Center, 1994. http://dx.doi.org/10.21236/ada280052.

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