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

Critical Research on Adjusting the Penalized Term for the Regularized Regression Models | Chapter 7 | Theory and Practice of Mathematics and Computer Science Vol.2

 

As a result of exiting high-dimensional ill-posed results, more attention has been provided to regularisation methods in the last two decades. To obtain more meaningful predictors, a smaller subset of large numbers of predictors is required. A new way of incorporating the penalised concept in regularised regression is proposed in this paper. The proposed penalty is based on using the variances of the regression parameters from the least square estimator. Some penalised estimators such as ridge, lasso, and elastic net, which are used to resolve both the problem of multicollinearity and to select variables, are added to the proposed system. Using the average mean squared error criterion (AMSE), good results are achieved. For simulated details, the best results in the simulated data are also seen in real data.  The type of the resulting estimators' lower average prediction errors (APE).

Author (s) Details

Magda M. M. Haggag
Department of Statistics, Mathematics and Insurance, Faculty of Commerce, Damanhour University, Egypt.

View Book :- https://bp.bookpi.org/index.php/bpi/catalog/book/271