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Luk, F. T.
Overview
Works:  9 works in 10 publications in 2 languages and 10 library holdings 

Publication Timeline
.
Most widely held works by
F. T Luk
Towards a computationally feasible online voltage instability index by
A Tiranuchit(
Book
)
2 editions published in 1987 in English and held by 2 libraries worldwide
2 editions published in 1987 in English and held by 2 libraries worldwide
A systolic array for the linear time solution of Toeplitz systems of equations by
Australian National University(
Book
)
1 edition published in 1983 in English and held by 1 library worldwide
1 edition published in 1983 in English and held by 1 library worldwide
Some linear time algorithms for systolic arrays by
Australian National University(
Book
)
1 edition published in 1982 in English and held by 1 library worldwide
1 edition published in 1982 in English and held by 1 library worldwide
Computing the singular value decomposition on the ILLIAC iv by
Cornell University(
Book
)
1 edition published in 1980 in English and held by 1 library worldwide
In this paper, we study the computation of the singular value decomposition of a matrix on the ILLIAC IV computer. We describe the architecture of the machine and explain why the standard GolubReinsch algorithm is not applicable to this problem. We then present a onesided orthogonalization method which makes very efficient use of the parallel computing abilities of the ILLIAC machine. Our method is shown to be Jacobilike and numerically stable. Finally, a comparison of our method on the ILLIAC IV computer with the GolubReinsch algorithm on a conventional machine demonstrates the great potential of parallel computers in the important area of matrix computations.
1 edition published in 1980 in English and held by 1 library worldwide
In this paper, we study the computation of the singular value decomposition of a matrix on the ILLIAC IV computer. We describe the architecture of the machine and explain why the standard GolubReinsch algorithm is not applicable to this problem. We then present a onesided orthogonalization method which makes very efficient use of the parallel computing abilities of the ILLIAC machine. Our method is shown to be Jacobilike and numerically stable. Finally, a comparison of our method on the ILLIAC IV computer with the GolubReinsch algorithm on a conventional machine demonstrates the great potential of parallel computers in the important area of matrix computations.
Computation of the singular value decomposition using Mesh connected processors by
Cornell University(
Book
)
1 edition published in 1982 in Undetermined and held by 1 library worldwide
A cyclic Jacobi method for computing the singular value decomposition of an $mxn$ matrix $(m \geq n)$ using systolic arrays is proposed. The algorithm requires $O(n[superscript]{2})$ processors and $O(m + n \log n)$ units of time.
1 edition published in 1982 in Undetermined and held by 1 library worldwide
A cyclic Jacobi method for computing the singular value decomposition of an $mxn$ matrix $(m \geq n)$ using systolic arrays is proposed. The algorithm requires $O(n[superscript]{2})$ processors and $O(m + n \log n)$ units of time.
A systolic architecture for the singular value decomposition by
Cornell University(
Book
)
1 edition published in 1982 in English and held by 1 library worldwide
We propose a systolic architecture for computing a singular value decomposition of an m x n matrix, where $m \geq n$. Our algorithm is stable and requires only $O(mn)$ time on a linear array of $O(n)$ processors. Extensions to algorithms for twodimensional arrays are also discussed.
1 edition published in 1982 in English and held by 1 library worldwide
We propose a systolic architecture for computing a singular value decomposition of an m x n matrix, where $m \geq n$. Our algorithm is stable and requires only $O(mn)$ time on a linear array of $O(n)$ processors. Extensions to algorithms for twodimensional arrays are also discussed.
Some linear time algorithms for systolic arrays by
Cornell University(
Book
)
1 edition published in 1983 in English and held by 1 library worldwide
We survey some recent results on lineartime and almost lineartime algorithms for one and twodimensional systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree $n$ over a finite field can be computed in time $O(n)$ on a linear systolic array of $O(n)$ cells; similarly for the GCD of two $n$bit binary numbers. Assuming that the systolic cells can perform floatingpoint arithmetic, we show how $n$ by $n$ Toeplitz systems of linear equations can be solved in time $O(n)$ on a linear array of $O(n)$ cells, each of which has constant memory size (independent of $n$). Finally, we outline how a twodimensional array of $O(n)$ by $O(n)$ cells with nearestneighbor interconnections can be used to solve (to working accuracy) the eigenvalue problem for a symmetric real $n$ by $n$ matrix in time $O(nS(n))$. Here $S(n)$ is a slowlygrowing function of $n$; for practical purposes $S(n)$ can be regarded as a constant. In addition to their theoretical interest, these results can be implemented relatively easily and have potential applications in the areas of errorcorrecting codes, symbolic and algebraic computation, signal processing and image processing. For example, systolic GCD arrays for error correction have been implemented with the microprogrammable "PSC'' chip.
1 edition published in 1983 in English and held by 1 library worldwide
We survey some recent results on lineartime and almost lineartime algorithms for one and twodimensional systolic arrays. In particular, we show how the greatest common divisor (GCD) of two polynomials of degree $n$ over a finite field can be computed in time $O(n)$ on a linear systolic array of $O(n)$ cells; similarly for the GCD of two $n$bit binary numbers. Assuming that the systolic cells can perform floatingpoint arithmetic, we show how $n$ by $n$ Toeplitz systems of linear equations can be solved in time $O(n)$ on a linear array of $O(n)$ cells, each of which has constant memory size (independent of $n$). Finally, we outline how a twodimensional array of $O(n)$ by $O(n)$ cells with nearestneighbor interconnections can be used to solve (to working accuracy) the eigenvalue problem for a symmetric real $n$ by $n$ matrix in time $O(nS(n))$. Here $S(n)$ is a slowlygrowing function of $n$; for practical purposes $S(n)$ can be regarded as a constant. In addition to their theoretical interest, these results can be implemented relatively easily and have potential applications in the areas of errorcorrecting codes, symbolic and algebraic computation, signal processing and image processing. For example, systolic GCD arrays for error correction have been implemented with the microprogrammable "PSC'' chip.
A triangular processor array for computing the singular value decomposition by
Cornell University(
Book
)
1 edition published in 1984 in English and held by 1 library worldwide
A triangular processor array for computing a singular value decomposition (SVD) of an $m \times n (m \geq n)$ matrix is proposed. A Jacobitype algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form. The requirements are $O(m)$ time and $1/4 n[superscript]{2} + O(n)$ processors.
1 edition published in 1984 in English and held by 1 library worldwide
A triangular processor array for computing a singular value decomposition (SVD) of an $m \times n (m \geq n)$ matrix is proposed. A Jacobitype algorithm is used to first triangularize the given matrix and then diagonalize the resultant triangular form. The requirements are $O(m)$ time and $1/4 n[superscript]{2} + O(n)$ processors.
The solution of singular value problems using systolic arrays by
Cornell University(
Book
)
1 edition published in 1984 in English and held by 1 library worldwide
This paper contains the computation of the singular value decomposition using systolic arrays. Two different linear time algorithms are presented.
1 edition published in 1984 in English and held by 1 library worldwide
This paper contains the computation of the singular value decomposition using systolic arrays. Two different linear time algorithms are presented.
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