• Journal of applied mathematics & informatics
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• v.5 no.3
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• pp.849-857
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• 1998

In this paper we have a concern on the Moore-Penrose inverse of two kinds of partitioned matrices of the form [V X] and [{{{{ {V atop {X} {{{{ {X atop { 0} }}] where V is symmetric. The Moore-Penrose inverse of the partitioned matrices can be reduced to be simpler forms according to some algebraic conditions. Firstly we investigate the representations of the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Moore-Penrose inverses of the partitioned matrices under four al-gebraic conditions. Each condition reduces the Morre-Penrose inverse into some simpler form. Also equivalant conditions will be considered. Finally we will perform a simulation study to investigate which con-dition is the most important in the sense that which condition occurs the most frequently in the real situation. The simluation study will show us a particular condition occurs the most likely tha other conditions. This fact enables us to obtain the Morre-Penrose inverse with less computational efforts and computational storage.

• Bulletin of the Korean Mathematical Society
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• v.48 no.5
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• pp.969-990
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• 2011

Assume that X, partitioned into $2{\times}2$ block form, is a solution of the system of quaternion matrix equations $A_1XB_1$ = $C_1,A_2XB_2=C_2$. We in this paper give the maximal and minimal ranks of the submatrices in X, and establish necessary and sufficient conditions for the submatrices to be zero, unique as well as independent. As applications, we consider the common inner inverse G, partitioned into $2{\times}2$ block form, of two quaternion matrices M and N. We present the formulas of the maximal and minimal ranks of the submatrices of G, and describe the properties of the submatrices of G as well. The findings of this paper generalize some known results in the literature.

• The Journal of the Acoustical Society of Korea
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• v.23 no.4E
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• pp.103-107
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• 2004

In this Paper, we propose an algorithm called partitioned recursive least square (PRLS) that involves a procedure that partitions a large data matrix into small matrices, applies RLS scheme in each of the small sub matrices and assembles the whole size estimation vector by concatenation of the sub-vectors from RLS output of sub matrices. Thus, the algorithm should be less complex than the conventional RLS and maintain an almost compatible estimation performance.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.117-119
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• 2005

For large structural eigen-analysis, the whole structure is divided into some partitioned structures and through synthesis of partitioned structural model the eigen-data of structure can be obtained. In that case, eigenvalue problem consists of semidefinite mass matrix form because of displacement constraint condition. In this work the eigenvalue problem is considered by means of several method, determinant search and null space reduction method.

• The Journal of Information Technology
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• v.10 no.3
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• pp.33-45
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• 2007

Systolic Array Processor is used for designing the special purpose processor in Digital Signal Processing, Computer Graphics, Neural Network Applications etc., since it has the characteristic of parallelism, pipeline processing and architecture of regularity. But, in case of using general design method, it has intial waiting period as large as No. of PE-1. And if the connected system needs parallel and simultaneous outputs, processor has some problems of the performance, since it generates only one output at each clock in output state. So in this paper, one dimensional Systolic Array Processor that is designed according to the dependance of data and operations using the partitioned sub-matrix is proposed for the purpose of improving the performance. 1-D Systolic Array using 4 partitioned sub-matrix has efficient method in case of considering those two problems.

• Journal of the Korean Mathematical Society
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• v.42 no.4
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• pp.871-881
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• 2005

In 1977, Ganter and Teirlinck proved that any $2t\;\times\;2t$ matrix with 2t nonzero elements can be partitioned into four sub-matrices of order t of which at most two contain nonzero elements. In 1978, Kramer and Mesner conjectured that any $mt{\times}nt$ matrix with kt nonzero elements can be partitioned into mn submatrices of order t of which at most k contain nonzero elements. In 1995, Brualdi et al. showed that this conjecture is true if $m = 2,\;k\;\leq\;3\;or\;k\geq\;mn-2$. They also found a counterexample of this conjecture when m = 4, n = 4, k = 6 and t = 2. When t = 2, we show that this conjecture is true if $k{\leq}5$.

• The Korean Journal of Applied Statistics
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• v.5 no.1
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• pp.1-8
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• 1992

Using the partitioned matrices, we presents a method of analysis which are not needed inverse matrix for Hierarchical Group Divisible(HGD) designs whose treatments are composed of 2.2.2.

• Nuclear Engineering and Technology
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• v.55 no.6
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• pp.2172-2194
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• 2023

A variational nodal method (VNM) with unstructured-mesh is presented for solving steady-state and dynamic neutron diffusion equations. Orthogonal polynomials are employed for spatial discretization, and the stiffness confinement method (SCM) is implemented for temporal discretization. Coordinate transformation relations are derived to map unstructured triangular nodes to a standard node. Methods for constructing triangular prism space trial functions and identifying unique nodes are elaborated. Additionally, the partitioned matrix (PM) and generalized partitioned matrix (GPM) methods are proposed to accelerate the within-group and power iterations. Neutron diffusion problems with different fuel assembly geometries validate the method. With less than 5 pcm eigenvalue (k_eff) error and 1% relative power error, the accuracy is comparable to reference methods. In addition, a test case based on the kilowatt heat pipe reactor, KRUSTY, is created, simulated, and evaluated to illustrate the method's precision and geometrical flexibility. The Dodds problem with a step transient perturbation proves that the SCM allows for sufficiently accurate power predictions even with a large time-step of approximately 0.1 s. In addition, combining the PM and GPM results in a speedup ratio of 2-3.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.251-263
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• 2004

In this paper, algorithms for computing the minimal polynomial and the common minimal polynomial of resultant matrices over any field are presented by means of the approach for the Grobner basis of the ideal in the polynomial ring, respectively, and two algorithms for finding the inverses of such matrices are also presented. Finally, an algorithm for the inverse of partitioned matrix with resultant blocks over any field is given, which can be realized by CoCoA 4.0, an algebraic system over the field of rational numbers or the field of residue classes of modulo prime number. We get examples showing the effectiveness of the algorithms.

• The Transactions of the Korean Institute of Electrical Engineers
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• v.39 no.11
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• pp.1146-1152
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• 1990

Direct calculation algorithm for the nonzero elements of system matrix is suggested for a single machine connected to the infinite bus. Excitation system and power system stabilizer are included. When the system matrix is partitioned into 15 nonzero blocks, we can identify the location of nonzero elements and formula for each element. No matrix inversion and multiplication are necessary. Sensitivity coefficients with respect to controller parameters are suggested based on the structure of system matrix.