Related papers: Convergence properties of fixed-point search with …
In this paper, we introduce the notion of $\alpha$--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this…
The Fourier inversion of phased coherent diffraction patterns offers images without the resolution and depth-of-focus limitations of lens-based tomographic systems. We report on our recent experimental images inverted using recent…
This paper presents a detailed, numerical study on the performance of the standard phasing algorithms with random phase illumination (RPI). Phasing with high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique phasing…
We present a novel feature matching algorithm that systematically utilizes the geometric properties of features such as position, scale, and orientation, in addition to the conventional descriptor vectors. In challenging scenes with the…
Traditional phase-shifting interferometry technique cannot be used to measure time-varying phase distributions. But single shot techniques could resolve the problem. Many efforts have been made on the phase retrieval methods from a single…
Federated learning (FL) is a distributed learning paradigm that allows several clients to learn a global model without sharing their private data. In this paper, we generalize a primal dual fixed point (PDFP) \cite{PDFP} method to federated…
The mean shift iterative algorithm was proposed in 2006, for using the entropy as a stopping criterion. From then on, a theoretical base has been developed and a group of applications has been carried out using this algorithm. This paper…
We analyze a class of high-amplitude, high-frequency oscillatory systems in which periodicity occurs on two distinct time scales and establish the convergence of its trajectories to a suitably averaged system by recursively applying the…
In this paper, we provide a detailed analysis of the global convergence properties of an extensively studied and extremely effective fixed-point algorithm for the Kullback-Leibler approximation of spectral densities, proposed by Pavon and…
Generic quantum search algorithm searches for target entity in an unsorted database by repeatedly applying canonical Grover's quantum rotation transform to reach near the vicinity of the target entity. Thus, upon measurement, there is a…
This paper is about line search for the generalized alternating projections (GAP) method. This method is a generalization of the von Neumann alternating projections method, where instead of performing alternating projections, relaxed…
This paper presents a non-manual design engineering method based on heuristic search algorithm to search for candidate agents in the solution space which formed by artificial intelligence agents modeled on the base of bionics.Compared with…
We extend to $p$-uniformly convex spaces tools from the analysis of fixed point iterations in linear spaces. This study is restricted to an appropriate generalization of single-valued, pointwise $\alpha$-averaged mappings. Our main…
In this paper, we explore the non-asymptotic global convergence rates of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method implemented with exact line search. Notably, due to Dixon's equivalence result, our findings are also applicable to…
Recent empirical studies have identified fixed point iteration phenomena in deep neural networks, where the hidden state tends to stabilize after several layers, showing minimal change in subsequent layers. This observation has spurred the…
Gradient-based first-order convex optimization algorithms find widespread applicability in a variety of domains, including machine learning tasks. Motivated by the recent advances in fixed-time stability theory of continuous-time dynamical…
Grover's search algorithm is the optimal quantum algorithm that can search an unstructured database quadratically faster than any known classical algorithm. The role of entanglement and correlations in the search algorithm have been studied…
The objective of this paper is to derive the essential invariance and contraction properties for the geometric periodic systems, which can be formulated as a category of differential inclusions, and primarily rendered in the phase…
Multi-objective search means searching for any one of several objectives in an unstructured database. Grover's algorithm has quadratic acceleration in multi-objection search than classical ones. Iterated operator in Grover's algorithm is a…
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular, we establish contraction results for a method of this type…