Related papers: Weak convergence of the periodic multiplicative Se…
It is well known that sparse approximation problem is \textsf{NP}-hard under general dictionaries. Several algorithms have been devised and analyzed in the past decade under various assumptions on the \emph{coherence} $\mu$ of the…
A while loop tests a termination condition on every iteration. On a quantum computer, such measurements perturb the evolution of the algorithm. We define a while loop primitive using weak measurements, offering a trade-off between the…
Weak measurements have an increasing number of applications in contemporary quantum mechanics. They were originally described as a weak interaction that slightly entangled the translational degrees of freedom of a particle to its spin,…
Due to the reduced probability of successful post-selection, the weak-value amplification seems to be unavailable for the parameter-estimation. Here, we show theoretically that, some effects due to the weak interactions present only in the…
The least square solution of minimum norm of a rectangular linear system of equations can be found out iteratively by using matrix splittings. However, the convergence of such an iteration scheme arising out of a matrix splitting is…
This paper explores the well known approximation approach to decide weak bisimilarity of Basic Parallel Processes. We look into how different refinement functions can be used to prove weak bisimilarity decidable for certain subclasses. We…
In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal…
A quasivariety has the weak ES property when the epimorphisms between its finitely generated members are surjective. A characterization of quasivarieties with the weak ES property is obtained and a method for detecting failures of this…
We show that the weak convergence of the Douglas--Rachford algorithm for finding a zero of the sum of two maximally monotone operators cannot be improved to strong convergence. Likewise, we show that strong convergence can fail for the…
A technique is presented for multiplexing two ergodic measure preserving transformations together to derive a third limiting transformation. This technique is used to settle a question regarding rigidity of weak mixing transformations.…
We investigate the power of weak measurements in the framework of quantum state discrimination. First, we define and analyze the notion of weak consecutive measurements. Our main result is a convergence theorem whereby we demonstrate when…
Many real-world problems rely on finding eigenvalues and eigenvectors of a matrix. The power iteration algorithm is a simple method for determining the largest eigenvalue and associated eigenvector of a general matrix. This algorithm relies…
We first introduce the concept of weak random periodic solutions of random dynamical systems. Then, we discuss the existence of such periodic solutions. Further, we introduce the definition of weak random periodic measures and study their…
We exhibit rationally ergodic, weakly mixing measure preserving transformations which are not subsequence rationally weakly mixing and give a condition for smoothness of renewal sequences.
For the principal eigenvalue of discrete weighted $p$-Laplacian on the set of nonnegative integers, the convergence of an approximation procedure and the inverse iteration is proved. Meanwhile, in the proof of the convergence, the…
The purpose of this paper is to prove a weak convergence result for empirical processes indexed in general classes of functions and with an underlying $\alpha$-mixing sequence of random variables. In particular the uniformly boundedness…
We propose a splitting algorithm for solving a system of composite monotone inclusions formulated in the form of the extended set of solutions in real Hilbert spaces. The resluting algorithm is a an extension of the algorithm in [4]. The…
In this paper, we establish the theory of weak convergence (toward a normal distribution) for both single-chain and population stochastic approximation MCMC algorithms. Based on the theory, we give an explicit ratio of convergence rates for…
We say that an infinite word w is weak abelian periodic if it can be factorized into finite words with the same frequencies of letters. In the paper we study properties of weak abelian periodicity, its relations with balance and frequency.…
We propose a randomized algorithm to compute the log-partition function of weakly interacting fermions with polynomial runtime in both the system size and precision. Although weakly interacting fermionic systems are considered tractable for…