相关论文: Sequential Multidimensional Spectral Estimation
First, we extend the results of approximate matrix multiplication from the Frobenius norm to the spectral norm. Second, We develop a class of fast approximate generalized linear regression algorithms with respect to the spectral norm.…
Calibration of expensive simulation models involves an emulator based on simulation outputs generated across various parameter settings to replace the actual model. Noisy outputs of stochastic simulation models require many simulation…
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true only in the finite dimensional case. Known spectral results…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
These notes offer a unified introduction to spectral methods for the study of complex systems. They are intended as an operative manual rather than a theorem-proof textbook: the emphasis is on tools, identities, and perspectives that can be…
Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct…
The study of resonances of the Schr\"{o}dinger operator has a long-standing tradition in mathematical physics. Extensive theoretical investigations have explored the proximity of resonances to the real axis, their distribution, and bounds…
This paper presents a bicomplex version of the Spectral Decomposition Theorem on infinite dimensional bicomplex Hilbert spaces. In the process, the ideas of bounded linear operators, orthogonal complements and compact operators on bicomplex…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
Bernstein's theorem (also called Hausdorff--Bernstein--Widder theorem) enables the integral representation of a completely monotonic function. We introduce a finite completely monotonic function, which is a completely monotonic function…
In this paper, we propose a reflected forward-backward splitting algorithic framework for finding a zero of the sum of finitely many monotone op-erators, including maximally monotone operators, cocoercive operators, and monotone and…
We discuss a new neural network-based direction of arrival estimation scheme that tackles the estimation task as a multidimensional classification problem. The proposed estimator uses a classification chain with as many stages as the number…
A matrix optimization problem over an uncertain linear system on finite horizon (abbreviated as MOPUL) is studied, in which the uncertain transition matrix is regarded as a decision variable. This problem is in general NP-hard. By using the…
Integration over curved manifolds with higher codimension and, separately, discrete variants of continuous operators, have been two important, yet separate themes in harmonic analysis, discrete geometry and analytic number theory research.…
The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior…
Dimensional regularization of Euclidean momentum space integrals is a highly successful technique in renormalization of quantum field theories. While it yields a straightforward algorithmic method, with which to evaluate diagrams beyond…
In this article we focus on dynamic network data which describe interactions among a fixed population through time. We model this data using the latent space framework, in which the probability of a connection forming is expressed as a…
We study the problem of computing the matrix exponential of a block triangular matrix in a peculiar way: Block column by block column, from left to right. The need for such an evaluation scheme arises naturally in the context of option…
In this paper, we consider the composition of two independent processes : one process corresponds to position and the other one to time. Such processes will be called iterated processes. We first propose an algorithm based on the Euler…
Probabilistic operational semantics for a nondeterministic extension of pure lambda calculus is studied. In this semantics, a term evaluates to a (finite or infinite) distribution of values. Small-step and big-step semantics are both…