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15
A multilinear singular value decomposition
 SIAM J. Matrix Anal. Appl
, 2000
"... Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are ..."
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Abstract. We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higherorder tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, firstorder perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pairwise symmetric tensors.
EXTENT: A Portable Programming Environment for Designing and Implementing HighPerformance Block Recursive Algorithms
, 1994
"... EXTENT is an EXpert system for TENsor product formula Translation. In this paper we present a programming environment for automatic generation of parallel/vector programs from tensor product formulas. A tensor (Kronecker) product based programming methodology is used for designing high performance p ..."
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Cited by 22 (9 self)
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EXTENT is an EXpert system for TENsor product formula Translation. In this paper we present a programming environment for automatic generation of parallel/vector programs from tensor product formulas. A tensor (Kronecker) product based programming methodology is used for designing high performance programs on various architectures. In this programming methodology, block recursive algorithms such as the fast Fourier transform and Strassen's matrix multiplication algorithm are expressed as tensor product formulas involving tensor product and other matrix operations. A tensor product formula can be systematically translated to parallel and/or vector code for various parallel architectures. A prototype system which generates programs for the Cray YMP, Cray T3D, and Intel Paragon has been developed. Performance results for some generated programs are presented. Keywords: Parallel programming environment, Tensor (Kronecker) product, Block recursive algorithm, Parallel program synthesis. 1...
Structured Analysis Approaches for Large Markov Chains  A Tutorial
 Applied Numerical Mathematics
, 1996
"... The tutorial introduces structured analysis approaches for continuous time Markov chains (CTMCs) which are a means to extend the size of analyzable state spaces significantly compared with conventional techniques. It is shown how generator matrices of large CTMCs can be represented in a very compact ..."
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The tutorial introduces structured analysis approaches for continuous time Markov chains (CTMCs) which are a means to extend the size of analyzable state spaces significantly compared with conventional techniques. It is shown how generator matrices of large CTMCs can be represented in a very compact form, how this representation can be exploited in numerical solution techniques and how numerical analysis profits from this exploitation. Additionally, recent results covering implementation issues, tool support, and advanced analysis techniques are surveyed. 1 Introduction Analysis of continuous time Markov chains (CTMCs) is a well established approach to analyze the performance, dependability and performability of computer and communication systems. Systems are modeled using specification techniques like queueing networks (QNs), stochastic Petri nets (SPNs), formal specification techniques to mention only a few. Unfortunately, the size of CTMCs underlying most realistic examples can be ...
A Framework for Generating DistributedMemory Parallel Programs for Block Recursive Algorithms
 Journal of Parallel and Distributed Computing
, 1996
"... A framework for synthesizing communicationefficient distributedmemory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and Strassen’s matrix multiplication is presented. This framework is based on an algebraic representation of the algorithms, which involve ..."
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Cited by 14 (4 self)
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A framework for synthesizing communicationefficient distributedmemory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and Strassen’s matrix multiplication is presented. This framework is based on an algebraic representation of the algorithms, which involves the tensor (Kronecker) product and other matrix operations. This representation is useful in analyzing the communication implications of computation partitioning and data distributions. The programs are synthesized under two different target program models. These two models are based on different ways of managing the distribution of data for optimizing communication. The first model uses pointtopoint interprocessor communication primitives, whereas the second model uses data redistribution primitives involving collective alltomany communication. These two program models are shown to be suitable for different ranges of problem size. The methodology is illustrated by synthesizing communicationefficient programs for the FFT. This framework has been incorporated into the EXTENT system for automatic generation of parallel/vector programs for block recursive algorithms. © 1996 Academic Press, Inc. 1.
A comparative study of algorithms for solving seemingly unrelated regressions models. Computational Statistic & Data Analysis
, 2003
"... Abstract The computational e ciency of various algorithms for solving seemingly unrelated regressions (SUR) models is investigated. Some of the algorithms adapt known methods; others are new. The ÿrst transforms the SUR model to an ordinary linear model and uses the QR decomposition to solve it. Th ..."
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Cited by 8 (6 self)
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Abstract The computational e ciency of various algorithms for solving seemingly unrelated regressions (SUR) models is investigated. Some of the algorithms adapt known methods; others are new. The ÿrst transforms the SUR model to an ordinary linear model and uses the QR decomposition to solve it. Three others employ the generalized QR decomposition to solve the SUR model formulated as a generalized linear leastsquares problem. Strategies to exploit the structure of the matrices involved are developed. The algorithms are reconsidered for solving the SUR model after it has been transformed to one of smaller dimensions.
Parametrizing quantum states and channels
 Quantum Information Processing
, 2003
"... Abstract. This work describes one parametrization of quantum states and channels and several of its possible applications. This parametrization works in any dimension and there is an explicit algorithm which produces it. Included in the list of applications are a simple characterization of pure stat ..."
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Cited by 6 (1 self)
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Abstract. This work describes one parametrization of quantum states and channels and several of its possible applications. This parametrization works in any dimension and there is an explicit algorithm which produces it. Included in the list of applications are a simple characterization of pure states, an explicit formula for one additive entropic quantity which does not require knowledge of eigenvalues, and an algorithm which finds one Kraus operator representation for a quantum operation without recourse to eigenvalue and eigenvector calculations. 1.
A technique for overlapping computation and communication for block recursive algorithms
 CONCURRENCY: PRACT. EXPER.,VOL.10(2), 73–90 (1998)
, 1998
"... This paper presents a design methodology for developing efficient distributedmemory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and bitonic sort. This design methodology is specifically suited for most modern supercomputers having a distributedmemory a ..."
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Cited by 6 (1 self)
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This paper presents a design methodology for developing efficient distributedmemory parallel programs for block recursive algorithms such as the fast Fourier transform (FFT) and bitonic sort. This design methodology is specifically suited for most modern supercomputers having a distributedmemory architecture with a circuitswitched or wormhole routed mesh or a hypercube interconnection network. A mathematical framework based on the tensor product and other matrix operations is used for representing algorithms. Communicationefficient implementations with effectively overlapped computation and communication are achieved by manipulating the mathematical representation using the tensor product algebra. Performance results for FFT programs on the Intel Paragon are presented.
A simple and efficient parallel FFT algorithm using the BSP model
 PARALLEL COMPUT
, 2000
"... In this paper, we present a new parallel radix4 FFT algorithm based on the BSP model. Our parallel algorithm uses the groupcyclic distribution family, which makes it simple to understand and easy to implement. We show how to reduce the communication cost of the algorithm by a factor of three, in ..."
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Cited by 5 (0 self)
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In this paper, we present a new parallel radix4 FFT algorithm based on the BSP model. Our parallel algorithm uses the groupcyclic distribution family, which makes it simple to understand and easy to implement. We show how to reduce the communication cost of the algorithm by a factor of three, in the case that the input/output vector is in the cyclic distribution. We also show how to reduce computation time on computers with a cachebased architecture. We present performance results on a Cray T3E with up to 64 processors, obtaining reasonable efficiency levels for local problem sizes as small as 256 and very good efficiency levels for sizes larger than 2048.
Parallel Strategies for Solving SURE Models with Variance Inequalities and Positivity
 of Correlations Constraints,” Computational Economics
"... Abstract. The problem of computing estimates of parameters in SURE models with variance inequalities and positivity of correlations constraints is considered. Efficient algorithms that exploit the block bidiagonal structure of the data matrix are presented. The computational complexity of the main ..."
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Cited by 5 (4 self)
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Abstract. The problem of computing estimates of parameters in SURE models with variance inequalities and positivity of correlations constraints is considered. Efficient algorithms that exploit the block bidiagonal structure of the data matrix are presented. The computational complexity of the main matrix factorizations is analyzed. A compact method to solve the model with proper subset regressors is proposed.