相关论文: Quasilinearization Method and WKB

A novel adaptive filtering method called $q$-Volterra least mean square ($q$-VLMS) is presented in this paper. The $q$-VLMS is a nonlinear extension of conventional LMS and it is based on Jackson's derivative also known as $q$-calculus. In…

We develop a pivot-shifted Carleman linearization framework for quantum algorithms solving quadratic nonlinear ordinary differential equations. By shifting the dynamics by a pivot state prior to Carleman lifting, and combining this with a…

A quantum linear Boltzmann equation is proposed, constructed in terms of the operator-valued dynamic structure factor of the macroscopic system the test particle is interacting with. Due to this operator structure it is a non-Abelian linear…

A method is presented for obtaining rigorous error estimates for approximate solutions of the Riccati equation, with real or complex potentials. Our main tool is to derive invariant region estimates for complex solutions of the Riccati…

Quantum Computing offers a new paradigm for efficient computing and many AI applications could benefit from its potential boost in performance. However, the main limitation is the constraint to linear operations that hampers the…

Years ago S. Weinberg suggested the "Quasi-Particle" method (Q-P) for iteratively solving an integral equation, based on an expansion in terms of sturmian functions that are eigenfunctions of the integral kernel. An improvement of this…

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality…

In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung, have been…

The Wentzel-Kramers-Brillouin semiclassical method is formulated for quasiparticles with quartic-in-momentum dispersion which presents the simplest case of a soft energy-momentum dispersion. It is shown that matching wave functions in the…

This paper presents two efficient and stable algorithms for recovering phase factors in quantum signal processing (QSP), a crucial component of many quantum algorithms. The first algorithm, the ``Half Cholesky" method, which is based on…

In recent years, quaternion matrix completion (QMC) based on low-rank regularization has been gradually used in image de-noising and de-blurring.Unlike low-rank matrix completion (LRMC) which handles RGB images by recovering each color…

Using the simple case of Blasius similarity solution, we illustrate a recently developed general method that reduces a strongly nonlinear problem into a weakly nonlinear analysis. The basic idea is to find a quasi-solution $F_0$ that…

Quantum computing (QC) seems to show potential for application in machine learning (ML). In particular quantum kernel methods (QKM) exhibit promising properties for use in supervised ML tasks. However, a major disadvantage of kernel methods…

We present qlbm, a Python software package designed to facilitate the development, simulation, and analysis of Quantum Lattice Boltzmann Methods (QBMs). qlbm is a modular framework that introduces a quantum component abstraction hierarchy…

Kernel quantile regression (KQR) extends classical quantile regression to nonlinear settings using kernel methods, offering a powerful tool for modeling conditional distributions. However, its application to large-scale datasets remains…

Quantum machine learning (QML) is the spearhead of quantum computer applications. In particular, quantum neural networks (QNN) are actively studied as the method that works both in near-term quantum computers and fault-tolerant quantum…

In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea…

The WKB approach for finding quasinormal modes of black holes, suggested in [1] by Schutz and Will at the first order and later developed to higher orders [2-4], became popular during the past decades, because, unlike more sophisticated…

Computational fluid dynamics lies at the heart of many issues in science and engineering, but solving the associated partial differential equations remains computationally demanding. With the rise of quantum computing, new approaches have…

Solving linear systems is at the foundation of many algorithms. Recently, quantum linear system algorithms (QLSAs) have attracted great attention since they converge to a solution exponentially faster than classical algorithms in terms of…