相关论文: A note on transformed Fourier systems for the appr…

The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…

This note presents an online pseudospectral method for system identification using Chebyshev polynomial basis under aperiodic sampling. The system dynamics are approximated piecewise by introducing a sliding time window. The number of…

In this paper, we study the problem of multivariate $L_2$-approximation of functions belonging to a weighted Korobov space. We propose and analyze a median lattice-based algorithm, inspired by median integration rules, which have attracted…

We propose a new technique for constructing low-rank approximations of matrices that arise in kernel methods for machine learning. Our approach pairs a novel automatically constructed analytic expansion of the underlying kernel function…

Parametric modeling of non-stationary signals is addressed in this article. We present several models based on the characteristic features of the modeled signal, together with the methods for accurate estimation of model parameters.…

Nowadays, low-rank approximations of matrices are an important component of many methods in science and engineering. Traditionally, low-rank approximations are considered in unitary invariant norms, however, recently element-wise…

Photonic bandgap engineering using aperiodic lattices (ALs) is systematically studied. Up to now ALs have tended to be defined by specific formulae (e.g. Fibonacci, Cantor), and theories have neglected other useful ALs along with the vast…

We present a method for improving a Non Local Means operator by computing its low-rank approximation. The low-rank operator is constructed by applying a filter to the spectrum of the original Non Local Means operator. This results in an…

Bottom-Up Hidden Tree Markov Model is a highly expressive model for tree-structured data. Unfortunately, it cannot be used in practice due to the intractable size of its state-transition matrix. We propose a new approximation which lies on…

We compare the fixed-phase approximation with the better known, but closely related fixed-node approximation on several testing examples. We found that both approximations behave very similarly with the fixed-phase results being very close…

The reconstruction of high-dimensional sparse signals is a challenging task in a wide range of applications. In order to deal with high-dimensional problems, efficient sparse fast Fourier transform algorithms are essential tools. The second…

In this paper we propose efficient randomized fixed-precision techniques for low tubal rank approximation of tensors. The proposed methods are faster and more efficient than the existing fixed-precision algorithms for approximating the…

In many practical applications, spatial data are often collected at areal levels (i.e., block data) and the inferences and predictions about the variable at points or blocks different from those at which it has been observed typically…

Truncating the Fourier transform averaged by means of a generalized Hausdorff operator, we approximate the adjoint to that Hausdorff operator of the given function. We find the formulas for the rate of approximation in various metrics in…

We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L<N are available. If the ratio p=L/N is not close to 1,…

While recent advancements in foundation models have significantly impacted machine learning, rigorous tests on the performance of time series foundation models (TSFMs) remain largely underexplored. This paper presents an empirical study…

Approximating multivariate periodic functions in weighted Korobov spaces via rank-1 lattices is fundamentally limited by frequency aliasing. Existing optimal-rate methods rely on randomized constructions or large pre-computations. We…

The wide application of estimation techniques in system analysis enable us to best determine and understand the history of system states. This paper attempts to delineate the theory behind linear and non-linear estimation with a suitable…

Fixed-parameter algorithms, approximation algorithms and moderately exponential algorithms are three major approaches to algorithms design. While each of them being very active in its own, there is an increasing attention to the connection…

We consider a general method for the approximation of the distribution of a process conditioned to not hit a given set. Existing methods are based on particle system that are failable, in the sense that, in many situations , they are not…