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math.ST2026
Sturm-Liouville-Type Parity and Oscillation of a Cubic Spline Eigenbasis
Shih-Hao Huang, Jephian C. -H. Lin, ShengLi Tzeng +1
We study the eigen-structure of the penalty matrix arising from cubic smoothing splines on equally spaced knots. Using purely matrix-theoretic arguments, we show that its positive…
math.CO2026
The Strong Spectral Property and the Jacobian Method for Weighted Laplacian Matrices
Minerva Catral, Shaun Fallat, Himanshu Gupta +1
Strong matrix properties, roughly speaking, refer to generic conditions on a matrix such that its spectral perturbation and pattern perturbation interact nicely to cover a neighbor…