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Faster least squares approximation
 Numerische Mathematik
"... Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. Methods dating back to Gauss and Legendre find a solution in O(nd 2) time, where n is the number of constraints and d is the number of variables. We present two rand ..."
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Cited by 53 (13 self)
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Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. Methods dating back to Gauss and Legendre find a solution in O(nd 2) time, where n is the number of constraints and d is the number of variables. We present two
AND ACCURACY OF THE CHISQUARE APPROXIMATION
, 1969
"... The purposes of this study were to tabulate the exact cumulative probabilities for a multinomial such that expected frequencies vary from 1 to not less than 5 in the case where the expected frequencies are equal and to study the accuracy of the conventional chisquare goodnessoffit test. The table ..."
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. The tables of cumulative probabilities provide exact tests of goodnessoffit in small samples. They also serve as criteria for approximations to the multinomial other than the conventional chisquare test or as criteria for the effectiveness of corrections for that test. (Author/FL)
On the stability and accuracy of least squares approximations
 Foundations of Computational Mathematics 13
, 2013
"... We consider the problem of reconstructing an unknown function f on a domain X from samples of f at n randomly chosen points with respect to a given measure ρX. Given a sequence of linear spaces (Vm)m>0 with dim(Vm) = m ≤ n, we study the least squares approximations from the spaces Vm. It is well ..."
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Cited by 20 (2 self)
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We consider the problem of reconstructing an unknown function f on a domain X from samples of f at n randomly chosen points with respect to a given measure ρX. Given a sequence of linear spaces (Vm)m>0 with dim(Vm) = m ≤ n, we study the least squares approximations from the spaces Vm
Mathematik Faster least squares approximation
"... Abstract Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n ≫ d. Then, existing exact methods find a solution vec ..."
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Abstract Least squares approximation is a technique to find an approximate solution to a system of linear equations that has no exact solution. In a typical setting, one lets n be the number of constraints and d be the number of variables, with n ≫ d. Then, existing exact methods find a solution
Moving Least Squares Approximation on the Sphere
, 2001
"... . We introduce moving least squares approximation as an approximation scheme on the sphere. We prove error estimates and approximation orders. Finally, we show certain numerical results. x1. Introduction Recently, approximation on the sphere has become important because of its obvious applications ..."
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Cited by 3 (0 self)
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. We introduce moving least squares approximation as an approximation scheme on the sphere. We prove error estimates and approximation orders. Finally, we show certain numerical results. x1. Introduction Recently, approximation on the sphere has become important because of its obvious applications
Toward Approximate Moving Least Squares Approximation With Irregularly . . .
 COMPUTER METHODS IN APPLIED MECHANICS & ENGINEERING
, 2004
"... By combining the well known moving least squares approximation method and the theory of approximate approximations due to Maz'ya and Schmidt we are able to present an approximate moving least squares method which inherits the simplicity of Shepard's method along with the accuracy of higher ..."
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Cited by 5 (2 self)
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By combining the well known moving least squares approximation method and the theory of approximate approximations due to Maz'ya and Schmidt we are able to present an approximate moving least squares method which inherits the simplicity of Shepard's method along with the accuracy
2 Regularized Least Squares Approximation
"... However, many times it makes more sense to approximate the given data by a least squares fit. fasshauer@iit.edu MATH 590 – Chapter 19 Fall 2008Up to now we have looked only at interpolation. However, many times it makes more sense to approximate the given data by a least squares fit. This is especia ..."
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However, many times it makes more sense to approximate the given data by a least squares fit. fasshauer@iit.edu MATH 590 – Chapter 19 Fall 2008Up to now we have looked only at interpolation. However, many times it makes more sense to approximate the given data by a least squares fit
LEAST SQUARES APPROXIMATIONS OF POWER SERIES
"... The classical least squares solutions in C[−1,1] in terms of linear combinations of ultraspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond to recent results of U. Luther and G. Mastr ..."
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The classical least squares solutions in C[−1,1] in terms of linear combinations of ultraspherical polynomials are extended in order to estimate power series on (−1,1). Approximate rates of uniform and pointwise convergence are obtained, which correspond to recent results of U. Luther and G
VECTOR ORTHOGONAL POLYNOMIALS AND LEAST SQUARES APPROXIMATION
, 1995
"... We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg, Ha ..."
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Cited by 15 (6 self)
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We describe an algorithm for complex discrete least squares approximation, which turns out to be very efficient when function values are prescribed in points on the real axis or on the unit circle. In the case of polynomial approximation, this reduces to algorithms proposed by Rutishauser, Gragg
THE LEAST SQUARES APPROXIMATION TO T(f) FOR
"... For sale by the Clearinghouse for Federal Scientific ond Technical lnformation ..."
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For sale by the Clearinghouse for Federal Scientific ond Technical lnformation
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