244 research outputs found
UTV Tools:Matlab Templates for Rank-Revealing UTV Decompositions
published in Numerical Algorithms and the paper's text is reprinted here by kind permissio
UTV Tools:Matlab Templates for Rank-Revealing UTV Decompositions
We describe a Matlab 5.2 package for computing and modifying certain rank-revealing decompositions that have found widespread use in signal processing and other applications. The package focuses on algorithms for URV and ULV decompositions, collectively known as UTV decompositions. We include algorithms for the ULLV decomposition, which generalizes the ULV decomposition to a pair of matrices. For completeness a few algorithms for computation of the RRQR decomposition are also included. The software in this package can be used as is, or can be considered as templates for specialized implementations on signal processors and similar dedicated hardware platforms
FPGA Hardware Implementation of DOA Estimation Algorithm Employing LU Decomposition
In this paper, authors present their work on field-programmable gate array (FPGA) hardware implementation of proposed direction of arrival estimation algorithms employing LU factorization. Both L and U matrices were considered in computing the angle estimates. Hardware implementation was done on a Virtex-5 FPGA and its experimental verification was performed using National Instruments PXI platform which provides hardware modules for data acquisition, RF down-conversion, digitization, etc. A uniform linear array consisting of four antenna elements was deployed at the receiver. LabVIEW FPGA modules with high throughput math functions were used for implementing the proposed algorithms. MATLAB simulations of the proposed algorithms were also performed to validate the efficacy of the proposed algorithms prior to hardware implementation of the same. Both MATLAB simulation and experimental verification establish the superiority of the proposed methods over existing methods reported in the literature, such as QR decomposition-based implementations. FPGA compilation results report low resource usage and faster computation time compared with the QR-based hardware implementation. Performance comparison in terms of estimation accuracy, percentage resource utilization, and processing time is also presented for different data and matrix sizes
Determining Rank in the Presence of Error
The problem of determining rank in the presence of error occurs in a
number of applications. The usual approach is to compute a
rank-revealing decomposition and make a decision about the rank by
examining the small elements of the decomposition. In this paper we
look at three commonly use decompositions: the singular value
decomposition, the pivoted QR decomposition, and the URV
decomposition.
(Also cross-referenced as UMIACS-TR-92-108
Learning Gaussian Graphical Models with Observed or Latent FVSs
Gaussian Graphical Models (GGMs) or Gauss Markov random fields are widely
used in many applications, and the trade-off between the modeling capacity and
the efficiency of learning and inference has been an important research
problem. In this paper, we study the family of GGMs with small feedback vertex
sets (FVSs), where an FVS is a set of nodes whose removal breaks all the
cycles. Exact inference such as computing the marginal distributions and the
partition function has complexity using message-passing algorithms,
where k is the size of the FVS, and n is the total number of nodes. We propose
efficient structure learning algorithms for two cases: 1) All nodes are
observed, which is useful in modeling social or flight networks where the FVS
nodes often correspond to a small number of high-degree nodes, or hubs, while
the rest of the networks is modeled by a tree. Regardless of the maximum
degree, without knowing the full graph structure, we can exactly compute the
maximum likelihood estimate in if the FVS is known or in
polynomial time if the FVS is unknown but has bounded size. 2) The FVS nodes
are latent variables, where structure learning is equivalent to decomposing a
inverse covariance matrix (exactly or approximately) into the sum of a
tree-structured matrix and a low-rank matrix. By incorporating efficient
inference into the learning steps, we can obtain a learning algorithm using
alternating low-rank correction with complexity per
iteration. We also perform experiments using both synthetic data as well as
real data of flight delays to demonstrate the modeling capacity with FVSs of
various sizes
Matrix Decomposition Methods for Efficient Hardware Implementation of DOA Estimation Algorithms: A Performance Comparison
Matrix operations form the core of array signal processing algorithms such as those required for direction of arrival (DOA) angle estimation of radio frequency signals incident on an antenna array. In this paper, we present a performance comparison of matrix decomposition methods for efficient FPGA hardware implementation of DOA estimation algorithms. These methods are very important in subspace-based DOA estimation algorithms as they are used for signal space extraction. DOA estimation algorithms employing LU, LDL, Cholesky, and QR decomposition methods are implemented on a Xilinx Virtex-5 FPGA. These DOA estimation algorithms are simulated in LabVIEW as well as experimentally validated in real-time on a prototype testbed constructed using Universal Software Radio Peripheral (USRP) Software Defined Radio (SDR) platform from National Instruments. Performance comparison of these algorithms is made in terms of resources consumption, computation speed, and estimation accuracy
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