相关论文: Transcending The Least Squares
This paper presents a novel numerical optimisation method for infinite dimensional optimisation. The functional optimisation makes minimal assumptions about the functional and without any specific knowledge on the derivative of the…
The best-worst method is an increasingly popular approach to solving multi-criteria decision-making problems. However, the usual prioritisation techniques may result in an ordinal violation if the best (worst) alternative identified in the…
An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model…
We emphasize intertwining relations as a universal tool in constructing one-dimensional quasi-exactly solvable operators and offer their possible generalization to the multidimensional case. Considered examples include all quasi-exactly…
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective function can only be…
In this chapter we present the sums of Hermitian squares approach to noncommutative polynomial optimization problems. This is an extension of the sums of squares approach for polynomial optimization arising from real algebraic geometry. We…
Estimation of a quadratic functional over parameter spaces that are not quadratically convex is considered. It is shown, in contrast to the theory for quadratically convex parameter spaces, that optimal quadratic rules are often rate…
We propose and analyze a weighted greedy scheme for computing deterministic sample configurations in multidimensional space for performing least-squares polynomial approximations on $L^2$ spaces weighted by a probability density function.…
We consider mixtures of $k\geq 2$ Gaussian components with unknown means and unknown covariance (identical for all components) that are well-separated, i.e., distinct components have statistical overlap at most $k^{-C}$ for a large enough…
In this paper, a few dual least-squares finite element methods and their application to scalar linear hyperbolic problems are studied. The purpose is to obtain $L^2$-norm approximations on finite element spaces of the exact solutions to…
We propose a new class of goodness-of-fit tests for the inverse Gaussian distribution. The proposed tests are weighted $L^2$-type tests depending on a tuning parameter. We develop the asymptotic theory under the null hypothesis and under a…
A method for moving least squares interpolation and differentiation is presented in the framework of orthogonal polynomials on discrete points. This yields a robust and efficient method which can avoid singularities and breakdowns in the…
We present a least squares method for estimating parameters from measurements of event yields in the presence of background and crossfeed. We adopt a unified approach to incorporating the statistical and systematic uncertainties on the…
The purpose of this article is to give a short introduction to the concept of quasi-unitary equivalence of quadratic forms and its consequences. In particular, we improve an estimate concerning the transitivity of quasi-unitary equivalence…
As non-institutive polynomial chaos expansion (PCE) techniques have gained growing popularity among researchers, we here provide a comprehensive review of major sampling strategies for the least squares based PCE. Traditional sampling…
Adaptive rational interpolation has been designed in the context of image processing as a new nonlinear technique that avoids the Gibbs phenomenon when we approximate a discontinuous function. In this work, we present a generalization to…
Let $\Omega$ be an open half-space or slab in $\mathbb{R}^{n+1}$ endowed with a perturbation of the Gaussian measure of the form $f(p):=\exp(\omega(p)-c|p|^2)$, where $c>0$ and $\omega$ is a smooth concave function depending only on the…
In this paper we demonstrate how the recently reported exactly and quasi-exactly solvable models admitting quasinormal modes can be constructed and classified very simply and directly by the newly proposed prepotential approach. These new…
We consider the problem of ranking $N$ objects starting from a set of noisy pairwise comparisons provided by a crowd of equal workers. We assume that objects are endowed with intrinsic qualities and that the probability with which an object…
We investigate the connections between max-weight approaches and dual subgradient methods for convex optimisation. We find that strong connections exist and we establish a clean, unifying theoretical framework that includes both max-weight…