20,738 research outputs found
A new family of approximate QR-LS algorithms for adaptive filtering
The 13th IEEE / S P Workshop on Statistical Signal Processing, Bordeaux, France, 17-20 July 2005This paper proposes a new family of approximate QR-based least squares (LS) adaptive filtering algorithms called p-TA-QR-LS algorithms. It extends the TA-QR-LS algorithm [6] by retaining different number of diagonal plus off-diagonals (denoted by an integer p) of the triangular factor of the augmented data matrix. For p=1 and N, it reduces respectively to the TA-QR-LS and the QR-RLS algorithms. It not only provides a link between the QR-LMS-type and the QR-RLS algorithms through a well-structured family of algorithms, but also offers flexible complexity-performance tradeoffs in practical implementation. These results are verified by computer simulation and the mean convergence of the algorithms is also analyzed. © 2005 IEEE.published_or_final_versio
Conversion of projected entangled pair states into a canonical form
We propose an algorithm to convert a projected entangled pair state (PEPS)
into a canonical form, analogous to the well-known canonical form of a matrix
product state. Our approach is based on a variational gauging ansatz for the QR
tensor decomposition of PEPS columns into a matrix product operator and a
finite depth circuit of unitaries and isometries. We describe a practical
initialization scheme that leads to rapid convergence in the QR optimization.
We explore the performance and stability of the variational gauging algorithm
in norm calculations for the transverse-field Ising and Heisenberg models on a
square lattice. We also demonstrate energy optimization within the PEPS
canonical form for the transverse-field Ising and Heisenberg models. We expect
this canonical form to open up improved analytical and numerical approaches for
PEPS.Comment: 8 pages, 6 Figure
Conversion of projected entangled pair states into a canonical form
We propose an algorithm to convert a projected entangled pair state (PEPS) into a canonical form, analogous to the well-known canonical form of a matrix product state. Our approach is based on a variational gauging ansatz for the QR tensor decomposition of PEPS columns into a matrix product operator and a finite depth circuit of unitaries and isometries. We describe a practical initialization scheme that leads to rapid convergence in the QR optimization. We explore the performance and stability of the variational gauging algorithm in norm calculations for the transverse-field Ising and Heisenberg models on a square lattice. We also demonstrate energy optimization within the PEPS canonical form for the transverse-field Ising and Heisenberg models. We expect this canonical form to open up improved analytical and numerical approaches for PEPS
Modelling the influence of non-minimum phase zeros on gradient based linear iterative learning control
The subject of this paper is modeling of the influence of non-minimum phase plant dynamics on the performance possible from gradient based norm optimal iterative
learning control algorithms. It is established that performance in the presence of right-half plane plant zeros typically has two phases. These consist of an initial
fast monotonic reduction of the L2 error norm followed by a very slow asymptotic convergence. Although the norm of the tracking error does eventually converge to zero, the practical implications over finite trials is apparent convergence to a non-zero error. The source of this slow convergence is identified and a model of this behavior as a (set of) linear constraint(s) is developed. This is shown to provide a good prediction of the magnitude of error norm where slow convergence begins. Formulae for this norm are obtained for single-input single-output systems with
several right half plane zeroes using Lagrangian techniques and experimental results are given that confirm the practical validity of the analysis
How long does it take to compute the eigenvalues of a random symmetric matrix?
We present the results of an empirical study of the performance of the QR
algorithm (with and without shifts) and the Toda algorithm on random symmetric
matrices. The random matrices are chosen from six ensembles, four of which lie
in the Wigner class. For all three algorithms, we observe a form of
universality for the deflation time statistics for random matrices within the
Wigner class. For these ensembles, the empirical distribution of a normalized
deflation time is found to collapse onto a curve that depends only on the
algorithm, but not on the matrix size or deflation tolerance provided the
matrix size is large enough (see Figure 4, Figure 7 and Figure 10). For the QR
algorithm with the Wilkinson shift, the observed universality is even stronger
and includes certain non-Wigner ensembles. Our experiments also provide a
quantitative statistical picture of the accelerated convergence with shifts.Comment: 20 Figures; Revision includes a treatment of the QR algorithm with
shift
- …