• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.705-720
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• 2001

We propose a variant of parallel block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factoriztion preconditioners for the corresponding somparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG using other types of block incomplete factorization preconditioners. Lastly, parallel computations of the block incomplete factorization preconditioners are carried out on the Cray C90.

• Bulletin of the Korean Mathematical Society
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• v.37 no.3
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• pp.551-568
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• 2000

We propose new parallelizable block incomplete factorization preconditioners for a symmetric block-tridiagonal H-matrix. Theoretical properties of these block preconditioners are compared with those of block incomplete factorization preconditioners for the corresponding comparison matrix. Numerical results of the preconditioned CG(PCG) method using these block preconditioners are compared with those of PCG method using a standard incomplete factorization preconditioner to see the effectiveness of the block incomplete factorization preconditioners.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.647-656
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• 2011

Incidence matrix is a useful tool for presenting incomplete block designs; however, it is inadequate to use only an incidence matrix in examining whether a certain incomplete block design becomes a balanced incomplete block design or not. We can use a structural matrix as a useful tool to show whether a certain incomplete block design becomes a balanced incomplete block design or not. We propose an augmented incidence matrix and ${\lambda}$ matrix as another tools for evaluating incomplete block designs. Through the augmented incidenc matrix and ${\lambda}$ matrix, we can ascertain whether a certain incomplete block design becomes a balance incomplete block design or not.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• Journal of the Korean Mathematical Society
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• v.36 no.1
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• pp.209-227
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• 1999

We propose new parallel block ILU (Incomplete LU) factorization preconditioners for a nonsymmetric block-tridiagonal M-matrix. Theoretial properties of these block preconditioners are studied to see the convergence rate of the preconditioned iterative methods, Lastly, numerical results of the right preconditioned GMRES and BiCGSTAB methods using the block ILU preconditioners are compared with those of these two iterative methods using a standard ILU preconditioner to see the effectiveness of the block ILU preconditioners.

• Journal of electromagnetic engineering and science
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• v.6 no.4
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• pp.244-252
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• 2006

A block Jacket transform and. its block inverse Jacket transformn have recently been reported in the paper 'Fast block inverse Jacket transform'. But the multiplication of the block Jacket transform and the corresponding block inverse Jacket transform is not equal to the identity transform, which does not conform to the mathematical rule. In this paper, new binary block Jacket transforms and the corresponding binary block inverse Jacket transforms of orders $N=2^k,\;3^k\;and\;5^k$ for integer values k are proposed and the mathematical proofs are also presented. With the aid of the Kronecker product of the lower order Jacket matrix and the identity matrix, the fast algorithms for realizing these transforms are obtained. Due to the simple inverse, fast algorithm and prime based $P^k$ order of proposed binary block inverse Jacket transform, it can be applied in communications such as space time block code design, signal processing, LDPC coding and information theory. Application of circular permutation matrix(CPM) binary low density quasi block Jacket matrix is also introduced in this paper which is useful in coding theory.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.641-651
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• 2011

In this paper, with use of the displacement matrix, two special matrices are constructed. By these special matrices the block decompositions of the block symmetric Hankel matrix and the inverse of the Hankel matrix are derived. Hence, the algorithms according to these decompositions are given. Furthermore, the numerical tests show that the algorithms are feasible.

• Bulletin of the Korean Mathematical Society
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• v.51 no.3
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• pp.765-771
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• 2014

Necessary and sufficient conditions for the existence of the group inverse of an anti-triangular block matrix in Banach algebras are presented. Using these results, we give the formulae for the generalized Drazin inverse of a block matrix.

• Communications of the Korean Mathematical Society
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• v.35 no.3
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• pp.917-925
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• 2020

It has been shown that the geometric mean A#B of positive definite Hermitian matrices A and B is the maximal element X of Hermitian matrices such that $$\(\array{A&X\\X&B}\)$$ is positive semi-definite. As an extension of this result for the 2 × 2 block matrix, we consider in this article the block matrix [[A#w_ijB]] whose (i, j) block is given by the Riemannian geodesics of positive definite Hermitian matrices A and B, where w_ij ∈ ℝ for all 1 ≤ i, j ≤ m. Under certain assumption of the Loewner order for A and B, we establish the equivalent condition for the parameter matrix ω = [w_ij] such that the block matrix [[A#w_ijB]] is positive semi-definite.

• The Korean Journal of Applied Statistics
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• v.2 no.1
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• pp.54-64
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• 1989

The paper by Kurkjian and Zelen(1963) introducted the Property A which related to a structural property of concordance matrix of the column incidence matrix. On the other hand, Paik(1985) showed the property of the concordance matrix, which has multinested block circulant pattern matrix, and this structural property was termed Property C by Paik(1985). This paper classifies the incomplete block designs according to the pattern of the concordence matrix which has multi-nested block circulant pattern. The purpose of this classification simplified the solution of reduced normal equation and plan of the design.