• Title/Summary/Keyword: matrix factorizations

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CONVERGENCE OF PARALLEL MULTISPLITTING METHODS USING ILU FACTORIZATIONS

  • Yun, Jae-Heon;Oh, Se-Young;Kim, Eun-Heui
    • Journal of applied mathematics & informatics
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    • v.15 no.1_2
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    • pp.77-90
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    • 2004
  • In this paper, we study the convergence of both relaxed multisplitting method and nonstationary two-stage multisplitting method associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is an H-matrix. Also, parallel performance results of nonstaionary two-stage multisplitting method using ILU factorizations as inner splittings on the IBM p690 supercomputer are provided to analyze theoretical results.

EQUIVARIANT MATRIX FACTORIZATIONS AND HAMILTONIAN REDUCTION

  • Arkhipov, Sergey;Kanstrup, Tina
    • Bulletin of the Korean Mathematical Society
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    • v.54 no.5
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    • pp.1803-1825
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    • 2017
  • Let X be a smooth scheme with an action of an algebraic group G. We establish an equivalence of two categories related to the corresponding moment map ${\mu}:T^{\ast}X{\rightarrow}g^{\ast}$ - the derived category of G-equivariant coherent sheaves on the derived fiber ${\mu}^{-1}(0)$ and the derived category of G-equivariant matrix factorizations on $T^{\ast}X{\times}g$ with potential given by ${\mu}$.

Relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods

  • 윤재헌
    • Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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    • 2003.09a
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    • pp.5.1-5
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    • 2003
  • In this paper, we study the convergence of relaxed multisplitting and relaxed nonstationary two-stage multisplitting methods associated with a multisplitting which is obtained from the ILU factorizations for solving a linear system whose coefficient matrix is an H-matrix. Also, parallel performance results of relaxed nonstaionary two-stage multisplitting method using ILU factorizations as inner splittings on the IBM p690 supercomputer are provided to analyze theoretical results.

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THE GENERALIZED PASCAL MATRIX VIA THE GENERALIZED FIBONACCI MATRIX AND THE GENERALIZED PELL MATRIX

  • Lee, Gwang-Yeon;Cho, Seong-Hoon
    • Journal of the Korean Mathematical Society
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    • v.45 no.2
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    • pp.479-491
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    • 2008
  • In [4], the authors studied the Pascal matrix and the Stirling matrices of the first kind and the second kind via the Fibonacci matrix. In this paper, we consider generalizations of Pascal matrix, Fibonacci matrix and Pell matrix. And, by using Riordan method, we have factorizations of them. We, also, consider some combinatorial identities.

COMPARISON OF MIRROR FUNCTORS OF ELLIPTIC CURVES VIA LG/CY CORRESPONDENCE

  • Lee, Sangwook
    • Journal of the Korean Mathematical Society
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    • v.57 no.5
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    • pp.1135-1165
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    • 2020
  • Polishchuk-Zaslow explained the homological mirror symmetry between Fukaya category of symplectic torus and the derived category of coherent sheaves of elliptic curves via Lagrangian torus fibration. Recently, Cho-Hong-Lau found another proof of homological mirror symmetry using localized mirror functor, whose target category is given by graded matrix factorizations. We find an explicit relation between these two approaches.

Weakly Right IQNN Rings

  • Yang Lee;Sang Bok Nam;Zhelin Piao
    • Kyungpook Mathematical Journal
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    • v.63 no.2
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    • pp.175-186
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    • 2023
  • In this article we look at the property of a 2 by 2 full matrix ring over the ring of integers, of being weakly right IQNN. This generalisation of the property of being right IQNN arises from products of idempotents and nilpotents. We shown that it is, indeed, a proper generalization of right IQNN. We consider the property of beign weakly right IQNN in relation to several kinds of factorizations of a free algebra in two indeterminates over the ring of integers modulo 2.

HYBRID REORDERING STRATEGIES FOR ILU PRECONDITIONING OF INDEFINITE SPARSE MATRICES

  • Lee Eun-Joo;Zgang Jun
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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    • pp.307-316
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    • 2006
  • Incomplete LU factorization preconditioning techniques often have difficulty on indefinite sparse matrices. We present hybrid reordering strategies to deal with such matrices, which include new diagonal reorderings that are in conjunction with a symmetric nondecreasing degree algorithm. We first use the diagonal reorderings to efficiently search for entries of single element rows and columns and/or the maximum absolute value to be placed on the diagonal for computing a nonsymmetric permutation. To augment the effectiveness of the diagonal reorderings, a nondecreasing degree algorithm is applied to reduce the amount of fill-in during the ILU factorization. With the reordered matrices, we achieve a noticeable improvement in enhancing the stability of incomplete LU factorizations. Consequently, we reduce the convergence cost of the preconditioned Krylov subspace methods on solving the reordered indefinite matrices.