Search results for "Linear"
showing 10 items of 7165 documents
Non-linear Local Polynomial Regression Multiresolution Methods Using $$\ell ^1$$-norm Minimization with Application to Signal Processing
2015
Harten’s Multiresolution has been developed and used for different applications such as fast algorithms for solving linear equations or compression, denoising and inpainting signals. These schemes are based on two principal operators: decimation and prediction. The goal of this paper is to construct an accurate prediction operator that approximates the real values of the signal by a polynomial and estimates the error using \(\ell ^1\)-norm in each point. The result is a non-linear multiresolution method. The order of the operator is calculated. The stability of the schemes is ensured by using a special error control technique. Some numerical tests are performed comparing the new method with…
Permutation Tests in Linear Regression
2015
Exact permutation tests are available only in rather simple linear models. The problem is that, although standard assumptions allow permuting the errors of the model, we cannot permute them in practice, because they are unobservable. Nevertheless, the residuals of the model can be permuted. A proof is given here which shows that it is possible to approximate the unobservable permutation distribution where the true errors are permuted by permuting the residuals. It is shown that approximation holds asymptotically and almost surely for certain quadratic statistics as well as for statistics which are expressible as the maximum of appropriate linear functions. The result is applied to testing t…
Determination of thermometric parameters from the conductance curve of the normal metal based tunnel junction array
1997
Abstract We propose a method for extracting thermometric parameters from the measured conductance curve, against bias voltage, of a tunnel junction array. Instead of fitting the whole theoretical conductance curve to the experiment, we perform several polynomial fits to selected bias regions. The advantages of this method is that polynomial fits are linear in their fitting parameters whereas the theoretical form for the conductance is inherently nonlinear. This way the proposed method is about three orders of magnitude faster than the nonlinear fit. Optimizing this polynomial fit procedure is discussed.
Matrix algebras with degenerate traces and trace identities
2022
In this paper we study matrix algebras with a degenerate trace in the framework of the theory of polynomial identities. The first part is devoted to the study of the algebra $D_n$ of $n \times n$ diagonal matrices. We prove that, in case of a degenerate trace, all its trace identities follow by the commutativity law and by pure trace identities. Moreover we relate the trace identities of $D_{n+1}$ endowed with a degenerate trace, to those of $D_n$ with the corresponding trace. This allows us to determine the generators of the trace T-ideal of $D_3$. In the second part we study commutative subalgebras of $M_k(F)$, denoted by $C_k$ of the type $F + J$ that can be endowed with the so-called st…
A new constructive method using the theory of invariants to obtain material behavior laws
2006
International audience; The aim of this paper is to present a constructive method to derive mechanical behavior laws using the Theory of Invariants and Continuum Thermodynamics. More precisely, we want to construct, in a general way, the state or dissipation potential in a polynomial form given a set of variables V and the material symmetry group S. For this purpose, we show how to obtain a set of generators for the S-invariant polynomials of V. Then, using the Grœbner basis concept, we write all the decompositions of a polynomial of a given degree.
On specific stability bounds for linear multiresolution schemes based on piecewise polynomial Lagrange interpolation
2009
Abstract The Deslauriers–Dubuc symmetric interpolation process can be considered as an interpolatory prediction scheme within Harten's framework. In this paper we express the Deslauriers–Dubuc prediction operator as a combination of either second order or first order differences. Through a detailed analysis of certain contractivity properties, we arrive to specific l ∞ -stability bounds for the multiresolution transform. A variety of tests indicate that these l ∞ bounds are closer to numerical estimates than those obtained with other approaches.
A family of higher-order single layer plate models meeting Cz0-requirements for arbitrary laminates
2019
Abstract In the framework of displacement-based equivalent single layer (ESL) plate theories for laminates, this paper presents a generic and automatic method to extend a basis higher-order shear deformation theory (polynomial, trigonometric, hyperbolic…) to a multilayer C z 0 higher-order shear deformation theory. The key idea is to enhance the description of the cross-sectional warping: the odd high-order C z 1 function of the basis model is replaced by one odd and one even high-order function and including the characteristic zig-zag behaviour by means of piecewise linear functions. In order to account for arbitrary lamination schemes, four such piecewise continuous functions are consider…
Polynomial Regression and Measurement Error
2020
Many of the phenomena of interest in information systems (IS) research are nonlinear, and it has consequently been recognized that by applying linear statistical models (e.g., linear regression), we may ignore important aspects of these phenomena. To address this issue, IS researchers are increasingly applying nonlinear models to their datasets. One popular analytical technique for the modeling and analysis of nonlinear relationships is polynomial regression, which in its simplest form fits a "U-shaped" curve to the data. However, the use of polynomial regression can be problematic when the independent variables are contaminated with measurement error, and the implications of error can be m…
Novel Computational Method for Harmonic Mitigation for Three-phase Five-level Cascaded H-Bridge Inverter
2018
The efficiency of the system is a very important parameter for high power electrical drives applications,. Moreover, in the system the efficiency of the power converter play a fundamental role and for this reason, the soft switching modulation techniques represent the best choice. This paper presents a novel computational method for harmonic mitigation on the output voltage of a five-level, three-phase Cascaded H-Bridge Inverter without solving non-linear equations. Through this simple approach the Working Areas have been identified in which the harmonics reference have minimum amplitude possible. Moreover, polynomial equations to evaluate the control angels have been found. In this way, th…
Zeroes of real polynomials on C(K) spaces
2007
AbstractFor a compact Hausdorff topological space K, we show that the function space C(K) must satisfy the following dichotomy: (i) either it admits a positive definite continuous 2-homogeneous real-valued polynomial, (ii) or every continuous 2-homogeneous real-valued polynomial vanishes in a non-separable closed linear subspace. Moreover, if K does not have the Countable Chain Condition, then every continuous polynomial, not necessarily homogeneous and with arbitrary degree, has constant value in an isometric copy of c0(Γ), for some uncountable Γ.