Acceleration of Fourier Series

نویسنده

  • Charles N. Moore
چکیده

We discuss the effects of several sequence acceleration methods on the partial sums of Fourier series. For a large set of functions we show that these methods fail. 2000 Mathematics Subject Classification: 65B10, 65T10, 42A20

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Fourier Series Acceleration and Hardy-littlewood Series

We discuss the effects of the δ2 and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even Hölder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.

متن کامل

Convergence acceleration of modified Fourier series in one or more dimensions

Modified Fourier series have recently been introduced as an adjustment of classical Fourier series for the approximation of nonperiodic functions defined on d-variate cubes. Such approximations offer a number of advantages, including uniform convergence. However, like Fourier series, the rate of convergence is typically slow. In this paper we extend Eckhoff’s method to the convergence accelerat...

متن کامل

0 ( 1998 ) ? { ? 1 An Asymptotically Hierarchy - consistent , Iterative Sequence Transformation for ConvergenceAcceleration of Fourier Series

We derive the I transformation, an iterative sequence transformation that is useful for the convergence acceleration of certain Fourier series. The derivation is based on the concept of hierarchical consistency in the asymptotic regime. We show that this sequence transformation is a special case of the J transformation. Thus, many properties of the I transformation can be deduced from the known...

متن کامل

Vibration measurement by temporal Fourier analyses of a digital hologram sequence.

A method for whole-field noncontact measurement of displacement, velocity, and acceleration of a vibrating object based on image-plane digital holography is presented. A series of digital holograms of a vibrating object are captured by use of a high-speed CCD camera. The result of the reconstruction is a three-dimensional complex-valued matrix with noise. We apply Fourier analysis and windowed ...

متن کامل

DELFT UNIVERSITY OF TECHNOLOGY REPORT 10-03 Acceleration of Option Pricing Technique on Graphics Processing Units

The acceleration of an option pricing technique based on Fourier cosine expansions on the Graphics Processing Unit (GPU) is reported. European options, in particular with multiple strikes, and Bermudan options will be discussed. The influence of the number of terms in the Fourier cosine series expansion, the number of strikes, as well as the number of exercise dates for Bermudan options, are ex...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009