Related papers: Extrapolation and Factorization
Notes of the lectures delivered in Les Houches during the Summer School on Complex Systems (July 2006).
Realization theory for operator colligations on Pontryagin spaces is used to study interpolation and factorization in generalized Schur classes. Several criteria are derived which imply that a given function is almost the restriction of a…
We look at two classical examples in the theory of numerical analysis, namely the Runge example for interpolation and Wilkinson's example (actually two examples) for rootfinding. We use the modern theory of backward error analysis and…
This paper gives a short survey of some basic results related to estimates of fractional integrals and Fourier transforms. It is closely adjoint to our previous survey papers \cite{K1998} and \cite{K2007}. The main methods used in the paper…
These lecture notes on Generalised Parton Distributions aim at providing a general picture of the field on the theoretical and phenomenological sides to master and Ph.D. students. They go along with the lecture given at the Baryon…
Notes from lectures given at the Autumn School on Algebraic and Arithmetic Geometry at the Johannes Gutenberg-Universit\"at Mainz in October 2017.
The lecture notes below correspond to the course given by the author in occasion of the VIASM school on Number Theory (18-24 June 2018, Hanoi). We have chosen to omit the proofs that are already presented in details in many references in…
In this note we mainly study the fine Jordan-Chevalley decomposition: a refinement of the classical Jordan-Chevalley decomposition of a matrix and we pay a particular attention to the field of the coefficients of the matrix. Moreover we…
Extrapolation is defined as making predictions beyond the range of the data used to estimate a statistical model. In ecological studies, it is not always obvious when and where extrapolation occurs because of the multivariate nature of the…
This paper is essentially a survey on several classical results of harmonic analysis and their recent extensions to Banach spaces. The first part of the paper is a summary of some important results in such topics as Bernstein spaces,…
The dominant cost in solving least-square problems using Newton's method is often that of factorizing the Hessian matrix over multiple values of the regularization parameter ($\lambda$). We propose an efficient way to interpolate the…
These are the handouts of an undergraduate minicourse at the Universit\`a di Bari, in the context of the 2017 INdAM Intensive Period "Contemporary Research in elliptic PDEs and related topics". Without any intention to serve as a throughout…
This is an expanded version of my Shaw Prize Lecture delivered at the Chinese University of Hong Kong.
These notes were originally written for the Stochastic Analysis Seminar in the Department of Operations Research and Financial Engineering at Princeton University, in February of 2011. The seminar was attended and supported by members of…
These are lecture notes on Floer and Rabinowitz-Floer homology written for a graduate course at UNICAMP August-December 2016 and a mini-course held at IMPA in August 2017.
We define extrapolation as any type of statistical inference on a conditional function (e.g., a conditional expectation or conditional quantile) evaluated outside of the support of the conditioning variable. This type of extrapolation…
This is an approximate reconstruction of the panel discussion on chiral extrapolation of physical observables. The session consisted of brief presentations from panelists, followed by responses from the panel, and concluded with questions…
In this present paper, I propose a derivation of unified interpolation and extrapolation function that predicts new values inside and outside the given range by expanding direct Taylor series on the middle point of given data set.…
These are expanded notes from lectures given at the \'{E}tats de la Recherche workshop on "Derived algebraic geometry and interactions". These notes serve as an introduction to the emerging theory of Poisson structures on derived stacks.
Science is facing a reproducibility crisis. Previous work has proposed incorporating data analysis replications into classrooms as a potential solution. However, despite the potential benefits, it is unclear whether this approach is…