Related papers: A simple way to speedup Gauss Elimination

We consider qubit purification under simultaneous continuous measurement of the three non-commuting qubit operators \sigma_x, \sigma_y, \sigma_z. The purification dynamics is quantified by (i) the average purification rate, and (ii) the…

Recently, a series of articles by Combes et al. has shown that it was possible to greatly improve the measurement rate of a register of qubits for given detector resources by means of a clever feedback control scheme. However, this speed-up…

Near-Gaussian probability densities are common in many important physical applications. Here we develop an asymptotic expansion methodology for computing entropic functionals for such densities. The expansion proposed is a close relative of…

Newton, in notes that he would rather not have seen published, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method that Euler did not recommend, that Legendre…

Sharpness-Aware Minimization (SAM) has emerged as a promising approach for effectively reducing the generalization error. However, SAM incurs twice the computational cost compared to base optimizer (e.g., SGD). We propose Asymptotic…

In this paper, we present an improved continued fraction approximation of the Wallis ratio. This approximation is fast in comparison with the recently discovered asymptotic series. We also establish the double-side inequality related to…

Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to…

Gaussian Quadrature is a well known technique for numerical integration. Recently Gaussian quadrature with respect to discrete measures corresponding to finite sums have found some new interest. In this paper we apply these ideas to…

A modification of the Gay-Berne potential is proposed which is about 10% to 20% more speed efficient (that is, the original potential runs 15% to 25% slower, depending on architecture) and statistically more accurate in reproducing the…

Wave-CAIPI MR imaging is a 3D imaging technique which can uniformize the g-factor maps and significantly reduce g-factor penalty at high acceleration factors. But it is time-consuming to calculate the average g-factor penalty for optimizing…

We present a variation on classic beam thresholding techniques that is up to an order of magnitude faster than the traditional method, at the same performance level. We also present a new thresholding technique, global thresholding, which,…

This paper presents an efficient method for implementing the Gaussian elimination technique for an nxm (m>=n) matrix, using a 2D SIMD array of nxm processors. The described algorithm consists of 2xn-1=O(n) iterations, which provides an…

The growth factor in Gaussian elimination measures how large the entries of an LU factorization can be relative to the entries of the original matrix. It is a key parameter in error estimates, and one of the most fundamental topics in…

An error bound for Gaussian Interpolation which is better than the current exponential-type error bound is presented.

3D Gaussian splatting (3DGS) has become a vital tool for learning a radiance field from multiple posed images. Although 3DGS shows great advantages over NeRF in terms of rendering quality and efficiency, it remains a research challenge to…

We propose a fast method for solving compressed sensing, Lasso regression, and Logistic Lasso regression problems that iteratively runs an appropriate solver using an active set approach. We design a strategy to update the active set that…

We provide an improved analysis of normalized SGD showing that adding momentum provably removes the need for large batch sizes on non-convex objectives. Then, we consider the case of objectives with bounded second derivative and show that…

Applying the exact renormalization group method to search the nonGaussian fixed points of gravitational coupling, is frequently followed by two steps: cutoff identification and improvement. Although there are various models for identifying…

The cumulative shrinkage process is an increasing shrinkage prior that can be employed within models in which additional terms are supposed to play a progressively negligible role. A natural application is to Gaussian factor models, where…

We present an accelerated pipeline, based on high-performance computing techniques and normalizing flows, for joint Bayesian parameter estimation and model selection and demonstrate its efficiency in gravitational wave astrophysics. We…