• Communications of the Korean Mathematical Society
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• v.19 no.2
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• pp.375-388
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• 2004

For solving symmetric systems of linear equations, it is shown that a new Krylov subspace method can be obtained. The new approach is one of the projection methods, and we call it the projection method for convenience in this paper. The projection method maintains the residual vector like simpler GMRES, symmetric QMR, SYMMLQ, and MINRES. By studying the quasiminimal residual method, we show that an extended projection method and the scaled symmetric QMR method are equivalent.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.457-473
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• 2005

In each step of the quasi-minimal residual (QMR) method which uses a look-ahead variant of the nonsymmetric Lanczos process to generate basis vectors for the Krylov subspaces induced by A, it is necessary to decide whether to construct the Lanczos vectors $v_{n+l}\;and\;w{n+l}$ as regular or inner vectors. For a regular step it is necessary that $D_k\;=\;W^{T}_{k}V_{k}$ is nonsingular. Therefore, in the floating-point arithmetic, the smallest singular value of matrix $D_k$, ${\sigma}_min(D_k)$, is computed and an inner step is performed if $\sigma_{min}(D_k)<{\epsilon}$, where $\epsilon$ is a suitably chosen tolerance. In practice it is absolutely impossible to choose correctly the value of the tolerance $\epsilon$. The subject of this paper is to show how discrete stochastic arithmetic remedies the problem of this tolerance, as well as the problem of the other tolerances which are needed in the other checks of the QMR method with the estimation of the accuracy of some intermediate results. Numerical examples are used to show the good numerical properties.

• Journal of the Chungcheong Mathematical Society
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• v.10 no.1
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• pp.57-70
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• 1997

In this paper two preconditioned GMRES and QMR methods are applied to the non-Hermitian system from the Petrov-Galerkin procedure for the Poisson equation and compared to each other. To our purpose the ILUT and the SSOR preconditioners are used.

• Proceedings of the KIEE Conference
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• 1996.07c
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• pp.1753-1755
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• 1996

This paper presents an analysis of the 3D microwave oven considering its forming. The results were compared with experimental data. Finite Element Method(FEM) using edge clement is employed for the analysis. For solving the large sparse system matrix equation was solved using the parallelized QMR method. Analysis of the 3d cavity has troublesome difficulties such as spurious solutions, too many memory and long computation time. We overcome this difficulties by using edge clement for spurious solutions and the parallelized QMR method by the aid of Paralle Virtual Machine(PVM) for the memory and computation time.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.3 no.2
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• pp.29-36
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• 1999

It is shown that a new Krylov subspace method for solving symmetric indefinite systems of linear equations can be obtained. We call the method as the projection method in this paper. The residual vector of the projection method is maintained at each iteration, which may be useful in some applications.

• Proceedings of the KIEE Conference
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• 1996.07c
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• pp.1741-1743
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• 1996

This paper presents simulations of the pancake in the simplified 3D microwave oven. The results were compared with experimental data. For the comparison we used infrared photography of the heated pancake and electric field distribution obtained by simulation. Finite Element Method (FEM) using edge element is employed for the simulation. For solving the large sparse system parallelled QMR method was used.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.2 no.2
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• pp.71-76
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• 1992

Piezoceramic filters were fabricated by adding $MnO_2 and FeZ0_3$ to the $0.05Pb(Al_{2/3}W_{1/3})O_3-0.95Pb(Zr_{0.52}Ti0.48)O_3$ system using photolithography method. As the amounts of $MnO_2$ increased, the electro-mechanical coupling factor(Kp) decresed. On the other hand, for $Fe_2O_3$ added samples, Kp was 57%, but mechanical quality factor(Qm) showed relatively low value. The passband widths were 155kHz for 0.3wt % $MnO_2$ addition and 260kHz for 0.1 wt % $Fe_2O_3$ addition, and were inversely propotional to Qm values. Group delay time characteristics showed Gausian for $MnO_2$ additions and Butterworth for$Fe_2O_3$ additions.