scholarly journals A Time-variant Norm Constrained Interpolation Problem Arising from Relaxed Commutant Lifting

2009 ◽  
pp. 139-166
Author(s):  
A. E. Frazho ◽  
S. ter Horst ◽  
M. A. Kaashoek
Keyword(s):  
Interpolation Problem ◽  
Constrained Interpolation ◽  
Commutant Lifting

Metric Constrained Interpolation, Commutant Lifting and Systems

1998 ◽  
Author(s):  
C. Foias ◽  
A. E. Frazho ◽  
I. Gohberg ◽  
M. A. Kaashoek
Keyword(s):  
Constrained Interpolation ◽  
Commutant Lifting

Bicubic partially blended rational fractal surface for a constrained interpolation problem

2016 ◽  
Vol 37 (1) ◽  
pp. 785-804 ◽  
Author(s):  
A. K. B. Chand ◽  
P. Viswanathan ◽  
N. Vijender
Keyword(s):  
Interpolation Problem ◽  
Fractal Surface ◽  
Constrained Interpolation

scholarly journals Lidstone–Euler Second-Type Boundary Value Problems: Theoretical and Computational Tools

2021 ◽  
Vol 18 (5) ◽  
Author(s):  
Francesco Aldo Costabile ◽  
Maria Italia Gualtieri ◽  
Anna Napoli
Keyword(s):  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence And Uniqueness ◽  
Interpolation Problem ◽  
Boundary Value ◽  
Computational Tools ◽  
Numerical Examples ◽  
Odd Order ◽  
Uniqueness Of The Solution ◽  
Type Boundary

AbstractGeneral nonlinear high odd-order differential equations with Lidstone–Euler boundary conditions of second type are treated both theoretically and computationally. First, the associated interpolation problem is considered. Then, a theorem of existence and uniqueness of the solution to the Lidstone–Euler second-type boundary value problem is given. Finally, for a numerical solution, two different approaches are illustrated and some numerical examples are included to demonstrate the validity and applicability of the proposed algorithms.

scholarly journals Application of Dynamically Constrained Interpolation Methodology in Simulating National-Scale Spatial Distribution of PM2.5 Concentrations in China

Atmosphere ◽  
2021 ◽  
Vol 12 (2) ◽  
pp. 272
Author(s):  
Ning Li ◽  
Junli Xu ◽  
Xianqing Lv
Keyword(s):  
Transport Model ◽  
Ground Level ◽  
Kriging Interpolation ◽  
Model Parameters ◽  
National Scale ◽  
Constrained Interpolation ◽  
Simulation Accuracy ◽  
Interpolation Accuracy ◽  
Geographical Regions ◽  
The Right

Numerous studies have revealed that the sparse spatiotemporal distributions of ground-level PM2.5 measurements affect the accuracy of PM2.5 simulation, especially in large geographical regions. However, the high precision and stability of ground-level PM2.5 measurements make their role irreplaceable in PM2.5 simulations. This article applies a dynamically constrained interpolation methodology (DCIM) to evaluate sparse PM2.5 measurements captured at scattered monitoring sites for national-scale PM2.5 simulations and spatial distributions. The DCIM takes a PM2.5 transport model as a dynamic constraint and provides the characteristics of the spatiotemporal variations of key model parameters using the adjoint method to improve the accuracy of PM2.5 simulations. From the perspective of interpolation accuracy and effect, kriging interpolation and orthogonal polynomial fitting using Chebyshev basis functions (COPF), which have been proved to have high PM2.5 simulation accuracy, were adopted to make a comparative assessment of DCIM performance and accuracy. Results of the cross validation confirm the feasibility of the DCIM. A comparison between the final interpolated values and observations show that the DCIM is better for national-scale simulations than kriging or COPF. Furthermore, the DCIM presents smoother spatially interpolated distributions of the PM2.5 simulations with smaller simulation errors than the other two methods. Admittedly, the sparse PM2.5 measurements in a highly polluted region have a certain degree of influence on the interpolated distribution accuracy and rationality. To some extent, adding the right amount of observations can improve the effectiveness of the DCIM around existing monitoring sites. Compared with the kriging interpolation and COPF, the results show that the DCIM used in this study would be more helpful for providing reasonable information for monitoring PM2.5 pollution in China.

Rethinking factor analysis as an interpolation problem

Statistics ◽  
1988 ◽  
Vol 19 (3) ◽  
pp. 359-367 ◽  
Author(s):  
A. Van der linde
Keyword(s):  
Factor Analysis ◽  
Interpolation Problem
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