• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제3권1호
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• pp.31-41
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• 1999

We investigate some techniques of iterative refinement of solutions of a nonsingular system Ax = b with A partitioned into blocks using only single precision arithmetic. We prove that iterative refinement improves a blockwise measure of backward stability. Some applications of the results for the least squares problem (LS) will be also considered.

• 대한전기학회논문지
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• 제40권4호
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• pp.331-341
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• 1991

The discrete cosine transform (DCT) is widely used in many signal processing areas, including image and speech data compression. In this paper, we investigate a fixed-point error analysis for fast DCT algorithms, namely, Lee [6], Hou [7] and Vetterli [8]. A statistical model for fixed-point error is analyzed to predict the output noise due to the fixed-point implementation. This paper deals with two's complement fixed-point data representation with truncation and rounding. For a comparison purpose, we also investigate the direct form DCT algorithm. We also propose a suitable scaling model for the fixed-point implementation to avoid an overflow occurring in the addition operation. Computer simulation results reveal that there is a close agreement between the theoretical and the experimental results. The result shows that Vetterli's algorithm is better than the other algorithms in terms of SNR.

• 대한전자공학회논문지SD
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• 제42권10호
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• pp.29-34
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• 2005

최대 양자화 오차는 W 비트 입력으로부터 W 비트의 곱을 출력하는 고정길이 곱셈기의 성능에 많은 영향을 준다. 본 논문에서는 고정길이 modified Booth 곱셈기의 오차범위를 분석한 후 최대오차를 줄이기 위해 추가해야 하는 칼럼 수를 결정하는 방법을 제안한다. 또한, 오차범위 분석방법이 reduced-width 곱셈기 디자인 시에도 적용할 수 있음을 보인다. 시뮬레이션을 통해 제안한 오차분석 방법이 고정길이 modified Booth 곱셈기의 실제 디자인에 유용하게 사용될 수 있음을 보인다.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제5권1호
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• pp.47-53
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• 2001

A problem of approximation by irrational splines is considered. These splines have a constant curvature between interpolation nodes and need only one additional boundary condition for derivatives, which should be set only at one of two boundary nodes, that is impossible for usual polynomial splines required boundary conditions at both boundary nodal points. Some estimations for numerical differentiation and rounding error analysis are presented.

• 전기학회논문지
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• 제56권2호
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• pp.428-431
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• 2007

A floating-point number system is used to represent a wide range of real numbers using finite number of bits. The standard the IEEE adopted in 1987 divides the range of real numbers into intervals of [$2^E,2^{E+1}$), where E is an Integer represented with finite bits, and defines equally spaced equal counts of discrete numbers in each interval. Since the numbers are defined discretely, not only the number representation itself includes errors but in floating-point arithmetic some strange behaviors are observed which cannot be agreed with the real world arithmetic. In this paper errors with floating-point number representation, those with arithmetic operations, and those due to order of arithmetic operations are analyzed theoretically with help of and verification with the results of some MATLAB program executions.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권2호
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• pp.171-188
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• 2015

In this paper, the efficient column-wise/row-wise lattice reduction (LR) updating and downdating methods are developed and their complexities are analyzed. The well-known LLL algorithm, developed by Lenstra, Lenstra, and Lov${\acute{a}}$sz, is considered as a LR method. When the column or the row is appended/deleted in the given lattice basis matrix H, the proposed updating and downdating methods modify the preconditioning matrix that is primarily computed for the LR with H and provide the initial parameters to reduce the updated lattice basis matrix efficiently. Since the modified preconditioning matrix keeps the information of the original reduced lattice bases, the redundant computational complexities can be eliminated when reducing the lattice by using the proposed methods. In addition, the rounding error analysis of the proposed methods is studied. The numerical results demonstrate that the proposed methods drastically reduce the computational load without any performance loss in terms of the condition number of the reduced lattice basis matrix.