151,552 research outputs found
On convergence of the maximum block improvement method
Abstract. The MBI (maximum block improvement) method is a greedy approach to solving optimization problems where the decision variables can be grouped into a finite number of blocks. Assuming that optimizing over one block of variables while fixing all others is relatively easy, the MBI method updates the block of variables corresponding to the maximally improving block at each iteration, which is arguably a most natural and simple process to tackle block-structured problems with great potentials for engineering applications. In this paper we establish global and local linear convergence results for this method. The global convergence is established under the Lojasiewicz inequality assumption, while the local analysis invokes second-order assumptions. We study in particular the tensor optimization model with spherical constraints. Conditions for linear convergence of the famous power method for computing the maximum eigenvalue of a matrix follow in this framework as a special case. The condition is interpreted in various other forms for the rank-one tensor optimization model under spherical constraints. Numerical experiments are shown to support the convergence property of the MBI method
On the Estimation of Nonrandom Signal Coefficients from Jittered Samples
This paper examines the problem of estimating the parameters of a bandlimited
signal from samples corrupted by random jitter (timing noise) and additive iid
Gaussian noise, where the signal lies in the span of a finite basis. For the
presented classical estimation problem, the Cramer-Rao lower bound (CRB) is
computed, and an Expectation-Maximization (EM) algorithm approximating the
maximum likelihood (ML) estimator is developed. Simulations are performed to
study the convergence properties of the EM algorithm and compare the
performance both against the CRB and a basic linear estimator. These
simulations demonstrate that by post-processing the jittered samples with the
proposed EM algorithm, greater jitter can be tolerated, potentially reducing
on-chip ADC power consumption substantially.Comment: 11 pages, 8 figure
Algorithmic patterns for -matrices on many-core processors
In this work, we consider the reformulation of hierarchical ()
matrix algorithms for many-core processors with a model implementation on
graphics processing units (GPUs). matrices approximate specific
dense matrices, e.g., from discretized integral equations or kernel ridge
regression, leading to log-linear time complexity in dense matrix-vector
products. The parallelization of matrix operations on many-core
processors is difficult due to the complex nature of the underlying algorithms.
While previous algorithmic advances for many-core hardware focused on
accelerating existing matrix CPU implementations by many-core
processors, we here aim at totally relying on that processor type. As main
contribution, we introduce the necessary parallel algorithmic patterns allowing
to map the full matrix construction and the fast matrix-vector
product to many-core hardware. Here, crucial ingredients are space filling
curves, parallel tree traversal and batching of linear algebra operations. The
resulting model GPU implementation hmglib is the, to the best of the authors
knowledge, first entirely GPU-based Open Source matrix library of
this kind. We conclude this work by an in-depth performance analysis and a
comparative performance study against a standard matrix library,
highlighting profound speedups of our many-core parallel approach
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