• Journal of applied mathematics & informatics
• /
• v.35 no.3_4
• /
• pp.399-411
• /
• 2017

We first provide the linear operator equations corresponding to the Tikhonov regularization image denoising problems with different regularization terms, and then we propose how to choose Kronecker product preconditioners which are required for accelerating the $G{\ell}$-PCG method. Next, we provide how to apply the $G{\ell}$-PCG method with Kronecker product preconditioner to the linear operator equations. Lastly, we provide numerical experiments for image denoisng problems to evaluate the effectiveness of the $G{\ell}$-PCG with Kronecker product preconditioner.

• Journal of applied mathematics & informatics
• /
• v.36 no.5_6
• /
• pp.531-540
• /
• 2018

We first show how to construct the linear operator equations corresponding to Tikhonov regularization problems for solving image deblurring problems with nearly separable point spread functions. We next propose a Kronecker product preconditioner which is suitable for the global PCG method. Lastly, we provide numerical experiments of the global PCG method with the Kronecker product preconditioner for several image deblurring problems to evaluate its effectiveness.

• Proceedings of the KIEE Conference
• /
• 1991.07a
• /
• pp.905-907
• /
• 1991

One of the general methods to diagnose abnormalities of heart is stethoscopy. This method needs special skill and experiment of doctors and it lacks for objectivity. Electrocardiography(ECG) is another biomedical method which is commonly used to diagnoss abnormalities of heart. The development of PCG is required in recent years to improve objectivity of stethoscopy method. In this paper, PCG is implemented on personal computer and ECG is also included to help the analysis of PCG waveform. Time analysis is used so far, but in this paper the frequency analysis is also considered to improve the accuracy of disgonosis. As future research, recognition of PCG and ECG signal and the Expert System is required to improve the accuracy of diagnosis.

• Journal of applied mathematics & informatics
• /
• v.36 no.3_4
• /
• pp.317-330
• /
• 2018

We first provide how to apply the global preconditioned conjugate gradient ($G{\ell}-PCG$) method with Kronecker product preconditioners to image deblurring problems with nearly separable point spread functions. We next provide a coarse-grained parallel image deblurring algorithm using the $G{\ell}-PCG$. Lastly, we provide numerical experiments for image deblurring problems to evaluate the effectiveness of the $G{\ell}-PCG$ with Kronecker product preconditioner by comparing its performance with those of the $G{\ell}-CG$, CGLS and preconditioned CGLS (PCGLS) methods.

• The Journal of Korean Institute of Communications and Information Sciences
• /
• v.31 no.8C
• /
• pp.786-794
• /
• 2006

We proposed a novel preconditioner based PCG(Preconditioned Conjugate Gradient) method for super resolution image reconstruction. Compared with the conventional block circulant type preconditioner, the proposed preconditioner can be more effectively applied for objective functions that include roughness penalty functions. The effectiveness of the proposed method was shown by simulations and experiments.

• Journal of applied mathematics & informatics
• /
• v.9 no.1
• /
• pp.331-339
• /
• 2002

A preconditioned conjugate gradient(PCG) scheme with the aid of deflation for computing a few of the smallest eigenvalues arid their corresponding eigenvectors of the large generalized eigenproblems is considered. Topically there are two types of deflation techniques, the deflation with partial shifts and an arthogonal deflation. The efficient way of determining partial shifts is suggested and the deflation-PCG schemes with various partial shifts are investigated. Comparisons of theme schemes are made with orthogonal deflation-PCG, and their asymptotic behaviors with restart operation are also discussed.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 1998.10a
• /
• pp.362-369
• /
• 1998

The computational environment in which engineers perform their designs has been rapidly evolved from coarse serial machines to massively parallel machines. Although the recent development of high-performance computers are available for a number of years, only limited successful applications of the new computational environments in computational structural engineering field has been reported due to its limited availability and large cost associated with high-performance computing. As a new computational model for high-performance engineering computing without cost and availability problems, parallel structural analysis models for large scale structures on a network of personal computers (PCs) are presented in this paper. In structural analysis solving routine for the linear system of equations is the most time consuming part. Thus, the focus is on the development of efficient preconditioned conjugate gradient (PCG) solvers on the proposed computational model. Two parallel PCG solvers, PPCG-I and PPCG-II, are developed and applied to analysis of large scale space truss structures.

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

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.495-509
• /
• 2002

We propose variants of the modified incomplete Cho1esky factorization preconditioner for a symmetric positive definite (SPD) matrix. Spectral properties of these preconditioners are discussed, and then numerical results of the preconditioned CG (PCG) method using these preconditioners are provided to see the effectiveness of the preconditioners.

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