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Reduced order model for parametric Boltzmann equation and its application to inverse problems
Shanyin Tong, Jingwei Hu, Fengyan Li +3
The Boltzmann equation plays an important role in modeling mesoscopic behavior in a wide range of scientific and engineering applications. However, its numerical solution is comput…
Structure-Preserving Reduced-Order Modeling via Low-Rank Transport Signatures
Jiajia Yu, Jingwei Hu, Fengyan Li +3
Parametrized PDEs with density-valued solutions are often difficult to approximate with classical linear reduced-order models, especially in transport-dominated regimes. We introdu…
The Optimal Linear B-splines Approximation via Kolmogorov Superposition Theorem and its Application
Ming-Jun Lai, Zhaiming Shen
We propose a new approach for approximating functions in via Kolmogorov superposition theorem (KST) based on the linear spline interpolation of the outer function in t…
Maximal Volume Matrix Cross Approximation for Image Compression and Least Squares Solution
Kenneth Allen, Ming-Jun Lai, Zhaiming Shen
We study the classic matrix cross approximation based on the maximal volume submatrices. Our main results consist of an improvement of the classic estimate for matrix cross approxi…
A Quasi-Orthogonal Matching Pursuit Algorithm for Compressive Sensing
Ming-Jun Lai, Zhaiming Shen
In this paper, we propose a new orthogonal matching pursuit algorithm called quasi-OMP algorithm which greatly enhances the performance of classical orthogonal matching pursuit (OM…