The ILL-Posedness of Derivative and Regularized Interpolation for Non-band limited Functions| Chapter 13 | Novel Research Aspects in Mathematical and Computer Science Vol. 4

The ill-posedness of derivative interpolation is examined in this study, as well as a regularised derivative interpolation for non-bandlimited signals. The convergence of regularised derivative interpolation is examined. The numerical results are shown, and they are compared to derivative interpolation using the Tikhonov regularisation method. The regularised derivative interpolation is more accurate in computation in this investigation. It is possible to use sampling-based regularised derivative interpolation. Some examples are used to establish and verify the convergence property. The numerical results are superior than those obtained using the Tikhonov regularisation approach.

Author(s) Details:

Weidong Chen,
Department of Mathematics, 460 McBryde Hall, Virginia Tech, 225 Stanger Street, Blacksburg, VA 24061-1026, US.

Please see the link here: https://stm.bookpi.org/NRAMCS-V4/article/view/7041

Determination of Derivative - and Regularized Derivative Interpolation for Band-limited Functions | Chapter 09 | Novel Research Aspects in Mathematical and Computer Science Vol. 2

 This chapter looks at the ill-posedness of derivative interpolation as well as a regularised derivative interpolation for band-limited signals. To check for ill-posedness, the Shannon Sampling Theorem is applied. A regularised Fourier transform and the Shannon Sampling Theorem are used to investigate the convergence of regularised derivative interpolation. The error estimation is provided, as well as high order derivatives. The regularised derivative interpolation algorithm is compared to various methods of derivative interpolation. To prove and test the convergence property, certain instances are given. The numerical results show that the regularised sampling algorithm's derivative interpolation is more successful in reducing noise for band-limited signals.

Author(S) Details

Weidong Chen
Department of Math, 460 McBryde Hall, Virginia Tech 225 Stanger Street, Blacksburg, VA 24061-1026, USA.


View Book:- https://stm.bookpi.org/NRAMCS-V2/article/view/6795