Accurate least-squares techniques using the orthogonal function approach
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Accurate least-squares techniques using the orthogonal function approach

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Published by Dept. of Commerce, National Oceanic and Atmospheric Administration, [Office of Oceanic and Atmospheric Services], Environmental Data and Information Service in Washington .
Written in English


  • Least squares -- Computer programs,
  • Functions, Orthogonal,
  • Time-series analysis

Book details:

Edition Notes

StatementJerry Sullivan, Center for Environmental Assessment Services
SeriesNOAA technical report ; EDIS 33
ContributionsUnited States. National Oceanic and Atmospheric Administration, United States. Environmental Data and Information Service, Center for Environmental Assessment Services (U.S.)
The Physical Object
Paginationiii, 104 p. :
Number of Pages104
ID Numbers
Open LibraryOL14851524M

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A unified approach is proposed for data modelling that includes supervised regression and classification applications as well as unsupervised probability density function estimation. The orthogonal-least-squares regression based on the leave-one-out test criteria is formulated within this unified data-modelling framework to construct sparse Cited by: Nov 21,  · This video provides an introduction to the concept of an orthogonal projection in least squares estimation. there will be a book: Least squares is a common method of conic fitting that minimizes the squared sum of a distance measure between a set of points and a conic. Orthogonal distance, when used as the distance that is. Jan 12,  · Orthogonal Least Squares Estimate on a plane, in the simple case of a linear equation, is in fact a problem that can be easily solved analytically Reviews: 5.

[−1,1]. The method uses the discrete orthogonal polynomial least squares (DOP-LS) ap-proximation based on the super Gaussian weight function, which is both smoothly con-nected to zero at ±1 and equals one in nearly the entire domain. As a result, the method has fast decaying expansion coefficients and also successfully suppresses Runge oscil-Cited by: Orthogonal Projections and Least Squares 1. Preliminaries We start out with some background facts involving subspaces and inner products. Definition Let U and V be subspaces of a vector space W such that U ∩V = {0}. The direct sum of U and V is the set U ⊕V = {u+v | . Keywords: Conic Fitting, Orthogonal Distance Least Squares Fitting. Abstract: Fitting of conics to a set of points is a well researched area and is used in many fields of science and engineer-ing. Least squares methods are one of the most popular techniques available for conic fitting and among these. have shown that least squares produces useful results. The computational techniques for linear least squares problems make use of orthogonal matrix factorizations. Models and Curve Fitting A very common source of least squares problems is curve fitting. Let t be the independent variable and let y(t) denote an unknown function of t that we want.

See linear least squares for a fully worked out example of this model.. A data point may consist of more than one independent variable. For example, when fitting a plane to a set of height measurements, the plane is a function of two independent variables, x and z, the most general case there may be one or more independent variables and one or more dependent variables at each data point. Iterative Selection Using Orthogonal Regression Techniques actually allows a fairly accurate estimation of the regres-sion function in such high dimensional low sample size using the least squares method, the backward selection method is typically not favored. A stepwise selection. then numerical techniques yield that the best fit value of a is and the best fit value of b is less than 10¡10 in absolute value. The difference between these values and those from the Method of Least Squares is in the best fit value of b(the least important of the two parameters), and is due to the different ways of weighting the. Overview of total least-squares methods This is motivated by the total least-squares (TLS) approach (Golub and Van Loan ) (also known as 'errors-in-variable regression' in the statistical.