# Luk, F. T.

Overview
Works: 9 works in 10 publications in 2 languages and 10 library holdings
Publication Timeline
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Most widely held works by F. T Luk
Towards a computationally feasible on-line voltage instability index by A Tiranuchit( Book )

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

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

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 Golub-Reinsch algorithm is not applicable to this problem. We then present a one-sided orthogonalization method which makes very efficient use of the parallel computing abilities of the ILLIAC machine. Our method is shown to be Jacobi-like and numerically stable. Finally, a comparison of our method on the ILLIAC IV computer with the Golub-Reinsch 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.
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 two-dimensional 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 linear-time and almost linear-time algorithms for one and two-dimensional 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 floating-point 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 two-dimensional array of $O(n)$ by $O(n)$ cells with nearest-neighbor 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 slowly-growing 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 error-correcting 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 Jacobi-type 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.

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