• Korean Management Science Review
• /
• v.19 no.2
• /
• pp.155-168
• /
• 2002

In this paper, some efficient implementation techniques for the multifrontal method, which can be used to compute the Cholesky factor of a symmetric positive definite matrix, are presented. In order to use the cache effect in the cache-based computer architecture, a hybrid method for factorizing a frontal matrix is considered. This hybrid method uses the column Cholesky method and the submatrix Cholesky method alternatively. Experiments show that the hybrid method speeds up the performance of the supernodal multifrontal method by 5%～10%, and it is superior to the Cholesky method in some problems with dense columns or large frontal matrices.

• Journal of Korean Institute of Industrial Engineers
• /
• v.24 no.3
• /
• pp.407-416
• /
• 1998

For fast Cholesky factorization, it is most important to reduce the number of nonzero elements by ordering methods. Generally, the minimum deficiency ordering produces less nonzero elements, but it is very slow. We propose an efficient implementation method. The minimum deficiency ordering requires much computations related to adjacent nodes. But, we reduce those computations by using indistinguishable nodes, the clique storage structures, and the explicit storage structures to compute deficiencies.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.41 no.1
• /
• pp.35-44
• /
• 2004

We Propose the methods to design the finite impulse response (FIR) and the infinite impulse response (IIR) lattice filters using Schur algorithm through the spectral factorization of the covariance matrix by circulant matrix factorization (CMF). Circulant matrix factorization is also very powerful tool used for spectral factorization of the covariance polynomial in matrix domain to obtain the minimum phase polynomial without the polynomial root finding problem. Schur algorithm is the method for a fast Cholesky factorization of Toeplitz matrix, which easily determines the lattice filter parameters. Examples for the case of the FIR filter and for the case of the In filter are included, and performance of our method check by comparing of our method and another methods (polynomial root finding and cepstral deconvolution).

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1991.10a
• /
• pp.24-24
• /
• 1991

• Proceedings of the KIEE Conference
• /
• 1996.07a
• /
• pp.68-70
• /
• 1996

In this paper, an efficient parallel computation method for solving large sparse systems of linear algebraic equations by using Cholesky's method in the finite element method is studied. The methods of minimizing the number of fill-ins in the factorization process of factorization are investigated for minimizing the amount of memory and computation time. The parallel programming is implemented under the PVM(Parallel Virtual Machine) environment. The method of load-distribution is studied for minimizing the computation time and the communication time.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1998.10a
• /
• pp.67-70
• /
• 1998

The computational speed of interior point method of linear programming depends on the speed of Cholesky factorization to solve AΘA$^{T}$ $\Delta$y=b. If the coefficient matrix A has dense columns then the matrix AΘA$^{T}$ becomes a dense matrix. This causes Cholesky factorization to be slow. The Schur complement method is applied to treat dense columns in many implementations but suffers from its numerical unstability. We study efficient implementation of Schur complement method. We achieve improvements in computational speed and numerical stability.rical stability.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 1999.04a
• /
• pp.311-312
• /
• 1999

• Korean Management Science Review
• /
• v.21 no.2
• /
• pp.43-60
• /
• 2004

Every iteration of interior-point methods of large scale optimization requires computing at least one orthogonal projection. In the practice, symmetric variants of the Gaussian elimination such as Cholesky factorization are accepted as the most efficient and sufficiently stable method. In this paper several specific implementation issues of the symmetric factorization that can be applied for solving such equations are discussed. The code called McSML being the result of this work is shown to produce comparably sparse factors as another implementations in the $MATLAB^{***}$ environment. It has been used for computing projections in an efficient implementation of self-regular based interior-point methods, McIPM. Although primary aim of developing McSML was to embed it into an interior-point methods optimizer, the code may equally well be used to solve general large sparse systems arising in different applications.

• Structural Engineering and Mechanics
• /
• v.62 no.3
• /
• pp.297-302
• /
• 2017

Structural reanalysis is frequently utilized to reduce the computational cost so that the process of design or optimization can be accelerated. The supports can be regarded as the design variables and may be modified in various types of structural optimization problems. The location, number, and type of supports can make a great impact on the performance of the structure. This paper presents a unified method for structural static reanalysis with imposition or relaxation of some support constraints. The information from the initial analysis has been fully utilized and the computational time can be significantly reduced. Numerical examples are used to validate the effectiveness of the proposed method.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.3 no.1
• /
• pp.99-106
• /
• 1999

An accelerated optimization technique combined with a stepwise deflation procedure is presented for the efficient evaluation of a few of the smallest eigenvalues and their corresponding eigenvectors of the generalized eigenproblems. The optimization is performed on the Rayleigh quotient of the deflated matrices by the aid of a preconditioned conjugate gradient scheme with the incomplete Cholesky factorization.