• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1175-1185
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• 1996

We study the computation of sparse null bases of equilibrium matrices in the context of structural optimization and incompressible fluid flow. In our approach we emphasize the parallel computatin and examine the applications. New block decomposition and node ordering schemes are suggested, and numerical examples are considered.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.32 no.12A
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• pp.1238-1243
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• 2007

The computational complexity for the zero-forcing (ZF)-based multiuser (MU) multiple-input multiple-output(MIMO) preprocessing matrices can be immoderately large as the number of transmit antennas or users increases. In this paper, we show that the span of singular vector space of a matrix can be obtained from the singular vectors of the parted rows of that matrix with computational saving and propose a computationally efficient recursive-algorithm for achieving the ZF-based preprocessing matrices. Analysis about the complexities shows that a new recursive-algorithm can lighten the computational load.

• Communications of the Korean Mathematical Society
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• v.15 no.1
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• pp.133-142
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• 2000

We consider some numerical solution methods for equilibrium equations Af + E$^{T}$ λ = r, Ef = s. Algebraic problems of this form evolve from many applications such as structural optimization, fluid flow, and circuits. An important approach, called the force method, to the solution to such problems involves dimension reduction nullspace computation for E. The purpose of this paper is to investigate the substructuring method for the solution step of the force method in the context of the incompressible fluid flow. We also suggests some iterative methods based upon substructuring scheme..

• The Journal of Korea Robotics Society
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• v.10 no.4
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• pp.230-244
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• 2015

Continuous-path motion control such as resolved motion rate control requires online solving of the inverse differential kinematics for a robot. However, the solution space of the inverse differential kinematics related to Jacobian J is not well-established. In this paper, the solution space of inverse differential kinematics is analyzed through categorization of mapping conditions between joint velocities and end-effector velocity of a robot. If end-effector velocity is within the column space of J, the solution or the minimum norm solution is obtained. If it is not within the column space of J, an approximate solution by least-squares is obtained. Moreover, this paper introduces an improved mapping diagram showing orthogonality and mapping clearly between subspaces, and concrete examples numerically showing the concept of several subspaces. Finally, a solver and graphics user interface (GUI) for inverse differential kinematics are developed using MATLAB, and the solution of inverse differential kinematics using the GUI is demonstrated for a vertically articulated robot.