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

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.

scholarly journals Test functions in constrained interpolation

2012 ◽  
Vol 364 (11) ◽  
pp. 5589-5604 ◽  
Author(s):  
Michael A. Dritschel ◽  
James Pickering
Keyword(s):  
Test Functions ◽  
Constrained Interpolation

A Proof of the Continuous Commutant Lifting Theorem

2000 ◽  
pp. 83-89 ◽  
Author(s):  
Ramon Bruzual ◽  
Marisela Dominguez
Keyword(s):  
Commutant Lifting ◽  
Commutant Lifting Theorem
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