Related papers: A survey of scalar and vector extrapolation
Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss-Seidel iterative solution of linear equations in the precision matrix. Specifically, the…
This article proposes new perspectives for developing derivative based numerical algorithms, supported by the introduction of a generalized derivative operators. It demonstrates that these operators have the potential to enhance and extend…
We consider the Cauchy problem for the 1D generalized Schr\"odinger equation on the whole axis. To solve it, any order finite element in space and the Crank-Nicolson in time method with the discrete transparent boundary conditions (TBCs)…
Approximate Bayesian computation (ABC) is a simulation-based likelihood-free method applicable to both model selection and parameter estimation. ABC parameter estimation requires the ability to forward simulate datasets from a candidate…
Product formulae are a popular class of digital quantum simulation algorithms due to their conceptual simplicity, low overhead, and performance which often exceeds theoretical expectations. Recently, Richardson extrapolation and polynomial…
We propose new primal-dual decomposition algorithms for solving systems of inclusions involving sums of linearly composed maximally monotone operators. The principal innovation in these algorithms is that they are block-iterative in the…
The problem of minimizing an objective that can be written as the sum of a set of $n$ smooth and strongly convex functions is considered. The Incremental Quasi-Newton (IQN) method proposed here belongs to the family of stochastic and…
In this paper we present a convergence rate analysis of inexact variants of several randomized iterative methods. Among the methods studied are: stochastic gradient descent, stochastic Newton, stochastic proximal point and stochastic…
Support vector data description (SVDD) is a machine learning technique that is used for single-class classification and outlier detection. The idea of SVDD is to find a set of support vectors that defines a boundary around data. When…
We present Cyqlone, a solver for linear systems with a stage-wise optimal control structure that fully exploits the various levels of parallelism available in modern hardware. Cyqlone unifies algorithms based on the sequential Riccati…
This paper deals with nonsmooth convex optimization problems in Euclidean spaces. We identify special elements of the subdifferential of a convex function, called specular gradients. Based on this observation, we propose three numerical…
We propose implicit integrators for solving stiff differential equations on unit spheres. Our approach extends the standard backward Euler and Crank-Nicolson methods in Cartesian space by incorporating the geometric constraint inherent to…
Gradient coding is a technique for straggler mitigation in distributed learning. In this paper we design novel gradient codes using tools from classical coding theory, namely, cyclic MDS codes, which compare favorably with existing…
This paper presents a simplified implementation of the arc-length method for computing the equilibrium paths of nonlinear structural mechanics problems using the finite element method. In the proposed technique, the predictor is computed by…
Industrial processes generate complex data that challenge fault detection systems, often yielding opaque or underwhelming results despite advanced machine learning techniques. This study tackles such difficulties using the Tennessee Eastman…
We establish linear convergence rates for a certain class of extrapolated fixed point algorithms which are based on dynamic string-averaging methods in a real Hilbert space. This applies, in particular, to the extrapolated simultaneous and…
We design and implement parallel prefix sum (scan) algorithms using Ascend AI accelerators. Ascend accelerators feature specialized computing units: the cube units for efficient matrix multiplication and the vector units for optimized…
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…
Since being analyzed by Rokhlin, Szlam, and Tygert and popularized by Halko, Martinsson, and Tropp, randomized Simultaneous Power Iteration has become the method of choice for approximate singular value decomposition. It is more accurate…
In this paper, we present a generic framework to extend existing uniformly optimal convex programming algorithms to solve more general nonlinear, possibly nonconvex, optimization problems. The basic idea is to incorporate a local search…