Polynomial Interpolation In Points Equidistributed On The Unit Circle
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Polynomial Interpolation In Points Equidistributed On The Unit Circle
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Author : J. H. Curtiss
language : en
Publisher:
Release Date : 1961
Polynomial Interpolation In Points Equidistributed On The Unit Circle written by J. H. Curtiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Interpolation categories.
A Stochastic Treatment Of Some Classical Interpolation Problems
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Author : J. H. Curtiss
language : en
Publisher:
Release Date : 1960
A Stochastic Treatment Of Some Classical Interpolation Problems written by J. H. Curtiss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Interpolation categories.
Polynomial Interpolation In Points Equidistributed On The Unit Circle
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Author :
language : en
Publisher:
Release Date : 1961
Polynomial Interpolation In Points Equidistributed On The Unit Circle written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Let Ln(f; z) be the polynomial of degree at most n-1 found by interpolation in the distinct points znk = ei nk, k = 1 ..., n, to a function f given on z = 1. It is known that a nece sary and sufficient condition that nlim Ln(f; z) = f(z), z 1, for all f analytic n z 1, is that nk be equidistributed on 0, 2 . In nonanalytic cases, convergence has been established when znk is an n-th root of unity, b t the behavior of Ln with other spacings of the interpolation points is not clear. It is here proved that if nk, k = 1 ..., n, are independent random variables each with a uniform probability distribution and if f satisfies certain mild smoothness restrictions on z = 1, then where Ln is found by interpolation to f in the random points znk = ei nk. A simple example is constructed involving an equidistributed sample seq ence nk for w ich Ln(f; z) diverges to infinity at each point z, z
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1967
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with categories.
Polynomial Interpolation In Points Equidistributed On The Unit Circle
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Author :
language : en
Publisher:
Release Date : 1961
Polynomial Interpolation In Points Equidistributed On The Unit Circle written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with categories.
Let Ln(f; z) be the polynomial of degree at most n-1 found by interpolation in the distinct points znk = ei nk, k = 1 ..., n, to a function f given on z = 1. It is known that a nece sary and sufficient condition that nlim Ln(f; z) = f(z), z 1, for all f analytic n z 1, is that nk be equidistributed on 0, 2 . In nonanalytic cases, convergence has been established when znk is an n-th root of unity, b t the behavior of Ln with other spacings of the interpolation points is not clear. It is here proved that if nk, k = 1 ..., n, are independent random variables each with a uniform probability distribution and if f satisfies certain mild smoothness restrictions on z = 1, then where Ln is found by interpolation to f in the random points znk = ei nk. A simple example is constructed involving an equidistributed sample seq ence nk for w ich Ln(f; z) diverges to infinity at each point z, z
Proceedings Of The Fourth Berkeley Symposium On Mathematical Statistics And Probability
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Author : Jerzy Neyman
language : en
Publisher: Univ of California Press
Release Date : 1961
Proceedings Of The Fourth Berkeley Symposium On Mathematical Statistics And Probability written by Jerzy Neyman and has been published by Univ of California Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1961 with Mathematical statistics categories.
Pacific Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1967
Pacific Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Mathematics categories.
Notices Of The American Mathematical Society
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Author : American Mathematical Society
language : en
Publisher:
Release Date : 1960
Notices Of The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Electronic journals categories.
Afosr
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Author : United States. Air Force. Office of Scientific Research
language : en
Publisher:
Release Date : 1960
Afosr written by United States. Air Force. Office of Scientific Research and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Research categories.
Information Processing Journal
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Author :
language : en
Publisher:
Release Date : 1962
Information Processing Journal written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Computers categories.