AI Article Synopsis
Article Abstract
In this paper, we investigate the simultaneous approximation of a function () and its derivative [Formula: see text] by Hermite interpolation operator [Formula: see text] based on Chevyshev polynomials. We also establish general theorem on extreme points for Hermite interpolation operator. Some results are considered to be an improvement over those obtained in Al-Khaled and Khalil (Numer Funct Anal Optim 21(5-6): 579-588, 2000), while others agrees with Pottinger's results (Pottinger in Z Agnew Math Mech 56: T310-T311, 1976).
Download full-text PDF |
Source |
|---|---|
| http://www.ncbi.nlm.nih.gov/pmc/articles/PMC5118382 | PMC |
| http://dx.doi.org/10.1186/s40064-016-3667-2 | DOI Listing |
Publication Analysis
Top Keywords
Similar Publications
Face Boundary Formulation for Harmonic Models: Face Image Resembling.
J Imaging
January 2025
Center for Pattern Recognition and Machine Intelligence, Concordia University, Montreal, QC H3G 1M8, Canada.
This paper is devoted to numerical algorithms based on harmonic transformations with two goals: (1) face boundary formulation by blending techniques based on the known characteristic nodes and (2) some challenging examples of face resembling. The formulation of the face boundary is imperative for face recognition, transformation, and combination. Mapping between the source and target face boundaries with constituent pixels is explored by two approaches: cubic spline interpolation and ordinary differential equation (ODE) using Hermite interpolation.
View Article and Find Full Text PDFStereo Bi-Telecentric Phase-Measuring Deflectometry.
Sensors (Basel)
September 2024
State Key Laboratory of Precision Measuring Technology and Instruments, Laboratory of Micro/Nano Manufacturing Technology, Tianjin University, Tianjin 300072, China.
Replacing the endocentric lenses in traditional Phase-Measuring Deflectometry (PMD) with bi-telecentric lenses can reduce the number of parameters to be optimized during the calibration process, which can effectively increase both measurement precision and efficiency. Consequently, the low distortion characteristics of bi-telecentric PMD contribute to improved measurement accuracy. However, the calibration of the extrinsic parameters of bi-telecentric lenses requires the help of a micro-positioning stage.
View Article and Find Full Text PDFOptimized Design of Direct Digital Frequency Synthesizer Based on Hermite Interpolation.
Sensors (Basel)
September 2024
College of Mechanical and Electrical Engineering, Henan University of Science and Technology, Luoyang 471000, China.
To address the issue of suboptimal spectral purity in Direct Digital Frequency Synthesis (DDFS) within resource-constrained environments, this paper proposes an optimized DDFS technique based on cubic Hermite interpolation. Initially, a DDFS hardware architecture is implemented on a Field-Programmable Gate Array (FPGA); subsequently, essential interpolation parameters are extracted by combining the derivative relations of sine and cosine functions with a dual-port Read-Only Memory (ROM) structure using the cubic Hermite interpolation method to reconstruct high-fidelity target waveforms. This approach effectively mitigates spurious issues caused by amplitude quantization during the DDFS digitalization process while reducing data node storage units.
View Article and Find Full Text PDFComparative analysis of parametric B-spline and Hermite cubic spline based methods for accurate ECG signal modeling.
J Electrocardiol
September 2024
Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh 491001, India.
Analyzing Electrocardiogram (ECG) signals is imperative for diagnosing cardiovascular diseases. However, evaluating ECG analysis techniques faces challenges due to noise and artifacts in actual signals. Machine learning for automatic diagnosis encounters data acquisition hurdles due to medical data privacy constraints.
View Article and Find Full Text PDFFrom low-rank retractions to dynamical low-rank approximation and back.
BIT Numer Math
June 2024
École Polytechnique Fédérale de Lausanne (EPFL) Institute of Mathematics, 1015 Lausanne, Switzerland.
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for other computational tasks on manifold as well, including interpolation tasks. In this work, we consider the application of retractions to the numerical integration of differential equations on fixed-rank matrix manifolds.
View Article and Find Full Text PDFWant AI Summaries of new PubMed Abstracts delivered to your In-box?
Enter search terms and have AI summaries delivered each week - change queries or unsubscribe any time!