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A stochastic algorithm is proposed, finding the set of generalized means associated to a probability measure on a compact Riemannian manifold M and a continuous cost function on the product of M by itself. Generalized means include p-means…

Probability · Mathematics 2013-05-28 Marc Arnaudon , Laurent Miclo

The Sturm sequence is generated by a pair of polynomials $P(x)$ and $P'(x)$, where $P(x)$ is assumed to have simple real roots. Euclidean algorithm generates then a finite sequence of polynomials orthogonal on the grid $x_s$ of roots of the…

Classical Analysis and ODEs · Mathematics 2019-04-09 Alexei Zhedanov

The coordinate descent method is an effective iterative method for solving large linear least-squares problems. In this paper, for the highly coherent columns case, we construct an effective coordinate descent method which iteratively…

Optimization and Control · Mathematics 2022-04-20 Li-Li Jin , Hou-Biao Li

This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…

Numerical Analysis · Mathematics 2018-10-30 Sharif Rahman

Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…

Metric Geometry · Mathematics 2018-07-30 Alexandru Popa

In this article, we derive Stein's method for approximating a spatial random graph by a generalised random geometric graph, which has vertices given by a finite Gibbs point process and edges based on a general connection function. Our main…

Probability · Mathematics 2024-11-06 Dominic Schuhmacher , Leoni Carla Wirth

Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…

Methodology · Statistics 2026-05-29 Ziyu Peng , Linglingzhi Zhu , Yao Xie

While an explicit basis is common in the study of Euclidean spaces, it is usually implied in the study of inertial relativistic systems. There are some conceptual advantages to including the basis in the study of special relativistic…

Classical Physics · Physics 2011-04-27 Peeter Joot

In this paper, we investigate a general class of stochastic gradient descent (SGD) algorithms, called Conditioned SGD, based on a preconditioning of the gradient direction. Using a discrete-time approach with martingale tools, we establish…

Statistics Theory · Mathematics 2023-10-17 Rémi Leluc , François Portier

The general inverse kinematics (IK) problem of a manipulator, namely that of acquiring the self-motion manifold (SMM) of all admissible joint angles for a desired end-effector pose, plays a vital role in robotics modeling, planning and…

Robotics · Computer Science 2021-04-27 Yajue Yang , Yuanqing Wu , Jia Pan

We describe an algorithm that, given any full-rank matrix A having fewer rows than columns, can rapidly compute the orthogonal projection of any vector onto the null space of A, as well as the orthogonal projection onto the row space of A,…

Numerical Analysis · Computer Science 2011-05-26 Vladimir Rokhlin , Mark Tygert

In this paper, a function on any pair of graphs is defined whose properties are similar to the properties of dot product in vector space. This function enables us to define graph orthogonality and, also, a new metric on isomorphism classes…

Combinatorics · Mathematics 2018-10-23 Ameneh Farhadian

We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…

Chaotic Dynamics · Physics 2022-04-28 Alan Rodrigo Mendoza Sosa , Atahualpa S. Kraemer

Given a finite, simple, vertex-weighted graph, we construct a graded associative (non-commutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to…

Algebraic Topology · Mathematics 2012-06-13 Peter Bubenik , Leah H. Gold

This paper deals with Gibbs samplers that include high dimensional conditional Gaussian distributions. It proposes an efficient algorithm that avoids the high dimensional Gaussian sampling and relies on a random excursion along a small set…

Computation · Statistics 2016-04-20 Olivier Féron , François Orieux , Jean-François Giovannelli

Symplectic vector-valued scalar product is constructed on the spaces of solutions of the real discrete Shrodinger equation with fixed value of the spectral parameter on graphs. It takes values in the first homology group of the graph. This…

Mathematical Physics · Physics 2007-05-23 S. P. Novikov

Generalized network tomography (GNT) deals with estimation of link performance parameters for networks with arbitrary topologies using only end-to-end path measurements of pure unicast probe packets. In this paper, by taking advantage of…

Statistics Theory · Mathematics 2012-10-31 Gugan Thoppe

We present some properties of measures (q-Gaussian) that orthogonalize the set of q-Hermite polynomials. We also present an algorithm for simulating i.i.d. sequences of random variables having q-Gaussian distribution.

Probability · Mathematics 2012-08-13 Paweł J. Szabłowki

Interior point methods solve small to medium sized problems to high accuracy in a reasonable amount of time. However, for larger problems as well as stochastic problems, one needs to use first-order methods such as stochastic gradient…

Optimization and Control · Mathematics 2016-10-14 Reza Takapoui , Hamid Javadi

A collection of subroutines and examples of their uses, as well as the underlying numerical methods, are described for generating orthogonal polynomials relative to arbitrary weight functions. The object of these routines is to produce the…

Classical Analysis and ODEs · Mathematics 2025-10-20 Walter Gautschi