3,937 research outputs found
Scalability Analysis of Parallel GMRES Implementations
Applications involving large sparse nonsymmetric linear systems encourage parallel implementations of robust iterative solution methods, such as GMRES(k). Two parallel versions of GMRES(k) based on different data distributions and using Householder reflections in the orthogonalization phase, and variations of these which adapt the restart value k, are analyzed with respect to scalability (their ability to maintain fixed efficiency with an increase in problem size and number of processors).A theoretical algorithm-machine model for scalability is derived and validated by experiments on three parallel computers, each with different machine characteristics
Knowledge-Aided STAP Using Low Rank and Geometry Properties
This paper presents knowledge-aided space-time adaptive processing (KA-STAP)
algorithms that exploit the low-rank dominant clutter and the array geometry
properties (LRGP) for airborne radar applications. The core idea is to exploit
the fact that the clutter subspace is only determined by the space-time
steering vectors,
{red}{where the Gram-Schmidt orthogonalization approach is employed to
compute the clutter subspace. Specifically, for a side-looking uniformly spaced
linear array, the} algorithm firstly selects a group of linearly independent
space-time steering vectors using LRGP that can represent the clutter subspace.
By performing the Gram-Schmidt orthogonalization procedure, the orthogonal
bases of the clutter subspace are obtained, followed by two approaches to
compute the STAP filter weights. To overcome the performance degradation caused
by the non-ideal effects, a KA-STAP algorithm that combines the covariance
matrix taper (CMT) is proposed. For practical applications, a reduced-dimension
version of the proposed KA-STAP algorithm is also developed. The simulation
results illustrate the effectiveness of our proposed algorithms, and show that
the proposed algorithms converge rapidly and provide a SINR improvement over
existing methods when using a very small number of snapshots.Comment: 16 figures, 12 pages. IEEE Transactions on Aerospace and Electronic
Systems, 201
Efficient Randomized Algorithms for the Fixed-Precision Low-Rank Matrix Approximation
Randomized algorithms for low-rank matrix approximation are investigated,
with the emphasis on the fixed-precision problem and computational efficiency
for handling large matrices. The algorithms are based on the so-called QB
factorization, where Q is an orthonormal matrix. Firstly, a mechanism for
calculating the approximation error in Frobenius norm is proposed, which
enables efficient adaptive rank determination for large and/or sparse matrix.
It can be combined with any QB-form factorization algorithm in which B's rows
are incrementally generated. Based on the blocked randQB algorithm by P.-G.
Martinsson and S. Voronin, this results in an algorithm called randQB EI. Then,
we further revise the algorithm to obtain a pass-efficient algorithm, randQB
FP, which is mathematically equivalent to the existing randQB algorithms and
also suitable for the fixed-precision problem. Especially, randQB FP can serve
as a single-pass algorithm for calculating leading singular values, under
certain condition. With large and/or sparse test matrices, we have empirically
validated the merits of the proposed techniques, which exhibit remarkable
speedup and memory saving over the blocked randQB algorithm. We have also
demonstrated that the single-pass algorithm derived by randQB FP is much more
accurate than an existing single-pass algorithm. And with data from a scenic
image and an information retrieval application, we have shown the advantages of
the proposed algorithms over the adaptive range finder algorithm for solving
the fixed-precision problem.Comment: 21 pages, 10 figure
Lanczos algorithm with Matrix Product States for dynamical correlation functions
The density-matrix renormalization group (DMRG) algorithm can be adapted to
the calculation of dynamical correlation functions in various ways which all
represent compromises between computational efficiency and physical accuracy.
In this paper we reconsider the oldest approach based on a suitable
Lanczos-generated approximate basis and implement it using matrix product
states (MPS) for the representation of the basis states. The direct use of
matrix product states combined with an ex-post reorthogonalization method
allows to avoid several shortcomings of the original approach, namely the
multi-targeting and the approximate representation of the Hamiltonian inherent
in earlier Lanczos-method implementations in the DMRG framework, and to deal
with the ghost problem of Lanczos methods, leading to a much better convergence
of the spectral weights and poles. We present results for the dynamic spin
structure factor of the spin-1/2 antiferromagnetic Heisenberg chain. A
comparison to Bethe ansatz results in the thermodynamic limit reveals that the
MPS-based Lanczos approach is much more accurate than earlier approaches at
minor additional numerical cost.Comment: final version 11 pages, 11 figure
A fast algorithm for LR-2 factorization of Toeplitz matrices
In this paper a new order recursive algorithm for the efficient â1 factorization of Toeplitz matrices is described. The proposed algorithm can be seen as a fast modified Gram-Schmidt method which recursively computes the orthonormal columns i, i = 1,2, âŠ,p, of , as well as the elements of Râ1, of a Toeplitz matrix with dimensions L Ă p. The factor estimation requires 8Lp MADS (multiplications and divisions). Matrix â1 is subsequently estimated using 3p2 MADS. A faster algorithm, based on a mixed and â1 updating scheme, is also derived. It requires 7Lp + 3.5p2 MADS. The algorithm can be efficiently applied to batch least squares FIR filtering and system identification. When determination of the optimal filter is the desired task it can be utilized to compute the least squares filter in an order recursive way. The algorithm operates directly on the experimental data, overcoming the need for covariance estimates. An orthogonalized version of the proposed â1 algorithm is derived. Matlab code implementing the algorithm is also supplied
Adaptive Nonlinear RF Cancellation for Improved Isolation in Simultaneous Transmit-Receive Systems
This paper proposes an active radio frequency (RF) cancellation solution to
suppress the transmitter (TX) passband leakage signal in radio transceivers
supporting simultaneous transmission and reception. The proposed technique is
based on creating an opposite-phase baseband equivalent replica of the TX
leakage signal in the transceiver digital front-end through adaptive nonlinear
filtering of the known transmit data, to facilitate highly accurate
cancellation under a nonlinear TX power amplifier (PA). The active RF
cancellation is then accomplished by employing an auxiliary transmitter chain,
to generate the actual RF cancellation signal, and combining it with the
received signal at the receiver (RX) low noise amplifier (LNA) input. A
closed-loop parameter learning approach, based on the decorrelation principle,
is also developed to efficiently estimate the coefficients of the nonlinear
cancellation filter in the presence of a nonlinear TX PA with memory, finite
passive isolation, and a nonlinear RX LNA. The performance of the proposed
cancellation technique is evaluated through comprehensive RF measurements
adopting commercial LTE-Advanced transceiver hardware components. The results
show that the proposed technique can provide an additional suppression of up to
54 dB for the TX passband leakage signal at the RX LNA input, even at
considerably high transmit power levels and with wide transmission bandwidths.
Such novel cancellation solution can therefore substantially improve the TX-RX
isolation, hence reducing the requirements on passive isolation and RF
component linearity, as well as increasing the efficiency and flexibility of
the RF spectrum use in the emerging 5G radio networks.Comment: accepted to IEE
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