Related papers: An algorithm for computing the multigraded Hilbert…
We present an algorithm for computing the integral closure of a reduced ring that is finitely generated over a finite field.
The explicit split-operator algorithm is often used for solving the linear and nonlinear time-dependent Schr\"{o}dinger equations. However, when applied to certain nonlinear time-dependent Schr\"{o}dinger equations, this algorithm loses…
We propose a primal-dual backward reflected forward splitting method for solving structured primal-dual monotone inclusion in real Hilbert space. The algorithm allows to use the inexact computations of the Lipschitzian and cocoercive…
An efficient proximal-gradient-based method, called proximal extrapolated gradient method, is designed for solving monotone variational inequality in Hilbert space. The proposed method extends the acceptable range of parameters to obtain…
Goldstein's 1977 idealized iteration for minimizing a Lipschitz objective fixes a distance - the step size - and relies on a certain approximate subgradient. That "Goldstein subgradient" is the shortest convex combination of objective…
A fast simulation algorithm for the calculation of multitime correlation functions of open quantum systems is presented. It is demonstrated that any stochastic process which ``unravels'' the quantum Master equation can be used for the…
A matrix-compression algorithm is derived from a novel isogenic block decomposition for square matrices. The resulting compression and inflation operations possess strong functorial and spectral-permanence properties. The basic observation…
The essential difficulty of gradient-based bilevel optimization using implicit differentiation is to estimate the inverse Hessian vector product with respect to neural network parameters. This paper proposes to tackle this problem by the…
A parallel splitting method is proposed for solving systems of coupled monotone inclusions in Hilbert spaces. Convergence is established for a wide class of coupling schemes. Unlike classical alternating algorithms, which are limited to two…
We explore the utilization of higher-order discretization techniques in optimizing the gate count needed for quantum computer based solutions of partial differential equations. To accomplish this, we present an efficient approach for…
We present a novel set of reversible modular multipliers applicable to quantum computing, derived from three classical techniques: 1) traditional integer division, 2) Montgomery residue arithmetic, and 3) Barrett reduction. Each multiplier…
Although application examples of multilevel optimization have already been discussed since the 1990s, the development of solution methods was almost limited to bilevel cases due to the difficulty of the problem. In recent years, in machine…
A consequent approach is proposed to construct symplectic force-gradient algorithms of arbitrarily high orders in the time step for precise integration of motion in classical and quantum mechanics simulations. Within this approach the basic…
The most widely used algorithm for floating point complex division, known as Smith's method, may fail more often than expected. This document presents two improved complex division algorithms. We present a proof of the robustness of the…
This paper presents a new fast iterative solver for large systems involving kernel matrices. Advantageous aspects of H2 matrix approximations and the multigrid method are hybridized to create the H2-MG algorithm. This combination provides…
Let $S$ be a multigraded polynomial ring such that the degree of each variable is a unit vector; so $S$ is the homogeneous coordinate ring of a product of projective spaces. In this setting, we characterize the formal Laurent series which…
An explicit multistep scheme is proposed for solving the initial-value Wigner problem. In this scheme, the integrated form of the Wigner equation is approximated by extrapolation or interpolation polynomials on backwards characteristics,…
Stratified digraphs are popular models for feedforward neural networks. However, computation of their path homologies has been limited to low dimensions due to high computational complexity. A recursive algorithm is proposed to compute…
This paper is to analyze the approximation solution of a split variational inclusion problem in the framework of infinite dimensional Hilbert spaces. For this purpose, several inertial hybrid and shrinking projection algorithms are proposed…
The partition function is an essential quantity in statistical mechanics, and its accurate computation is a key component of any statistical analysis of quantum system and phenomenon. However, for interacting many-body quantum systems, its…