相关论文: Iterations of the generalized Gram-Schmidt procedu…

A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is…

Consider a mean-reverting equation, generalized in the sense it is driven by a 1-dimensional centered Gaussian process with H\"older continuous paths on $[0,T]$ ($T > 0$). Taking that equation in rough paths sense only gives local existence…

We revisit the S-procedure for general functions with "geometrical glasses". We thus delineate a necessary condition, and almost a sufficient condition, to have the S-procedure valid. Everything is expressed in terms of convexity of…

Three algorithms of Gram-Schmidt type are given that produce an orthogonal decomposition of finite $d$-dimensional symmetric, alternating, or Hermitian forms over division rings. The first uses $d^3/3+O(d^2)$ ring operations with very…

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable,…

In this paper, we explain a new Iterative Method-Fixed Point and develop its convergence theory for finding approximate solutions of nonlinear equations in the setting of Banach spaces. First, we discuss the convergence analysis of our…

In this paper, we develop a new Randomized Global Generalized Minimum Residual (RGlGMRES) algorithm for efficiently computing solutions to large scale linear systems with multiple right hand sides.The proposed method builds on a recently…

Gaussian processes scale prohibitively with the size of the dataset. In response, many approximation methods have been developed, which inevitably introduce approximation error. This additional source of uncertainty, due to limited…

The randomized projection (RP) method is a simple iterative scheme for solving linear feasibility problems and has recently gained popularity due to its speed and low memory requirement. This paper develops an accelerated variant of the…

Guided image filtering (GIF) is a popular smoothing technique, in which an additional image is used as a structure guidance for noise removal with edge preservation. The original GIF and some of its subsequent improvements are derived from…

Gaussian Splatting (GS) has demonstrated impressive quality and efficiency in novel view synthesis. However, shape extraction from Gaussian primitives remains an open problem. Due to inadequate geometry parameterization and approximation,…

The generalized minimal residual (GMRES) algorithm is applied to image reconstruction using linear computed tomography (CT) models. The GMRES algorithm iteratively solves square, non-symmetric linear systems and it has practical application…

The generalized inverse Gaussian, denoted $\mathrm{GIG}(p, a, b)$, is a flexible family of distributions that includes the gamma, inverse gamma, and inverse Gaussian distributions as special cases. In addition to its applications in…

We introduce a scalable approach to Gaussian process inference that combines spatio-temporal filtering with natural gradient variational inference, resulting in a non-conjugate GP method for multivariate data that scales linearly with…

This paper proposes a parametric error analysis method for Goldschmidt floating point division, which reveals how the errors of the intermediate results accumulate and propagate during the Goldschmidt iterations. The analysis is developed…

This paper introduces a reformulation of the classical convergence theorem for spectral sequences of filtered complexes which provides an algorithm to effectively compute the induced filtration on the total (co)homology, as soon as the…

Generalized majority-minority (GMM) operations are introduced as a common generalization of near unanimity operations and Mal'tsev operations on finite sets. We show that every instance of the constraint satisfaction problem (CSP), where…

Since the seminal work of Mecke, Nagel and Weiss, the iteration stable (STIT) tessellations have attracted considerable interest in stochastic geometry as a natural and flexible yet analytically tractable model for hierarchical spatial…

In the generalized truncation construction, one replaces each vertex of a $k$-regular graph $\Gamma$ with a copy of a graph $\Upsilon$ of order $k$. We investigate the symmetry properties of the graphs constructed in this way, especially in…

The generalized parton distributions (GPDs) for the spin-3/2 $\Delta^+$ resonance are studied numerically by using a diquark spectator approach. Our results show that symmetric constraints from time reversal on GPDs are satisfied. The axial…