Yimin Zhong

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20232026

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math.NA2026

An improvement on B-spline basis condition number

Yimin Zhong

In this short note, we improve the upper bound on the condition number of the univariate B-spline basis of order $k$ from $k 2^{k}$ to $O (k lo g k 2^{k})$ for all $k \geq 2$ .

math.NA2026

From Frequency Bias to Spectral Balance: Operator-Aware Preconditioners for PINNs

Roy Y. He, Ying Liang, Hongkai Zhao +1

When neural networks (NNs) are used as a type of nonlinear parametric representation to solve partial differential equations (PDEs), they often display frequency-dependent learning…

math.NA2023

Error Analysis for the Implicit Boundary Integral Method

Yimin Zhong, Kui Ren, Olof Runborg +1

The implicit boundary integral method (IBIM) provides a framework to construct quadrature rules on regular lattices for integrals over irregular domain boundaries. This work provid…