Spectral Optimization

Spectral Optimization

When Spectral Convergence Fails for Smooth Data: The Hidden Role of Boundary Layers

You have smooth data — infinitely differentiable, even. The kind of function spectral methods were built for. Yet your Chebyshev expansion, that suppo...

Spectral Optimization

When Tiny Eigenvalue Shifts Crash Your Solver

Imagine you are solving a substantial eigenvalue issue for a bridge block. The solver converges— then a load shift by 0.1%. Your eigenpairs jump, and ...

Spectral Optimization

When Your Spectrum Lies: Aliasing in Non-Uniform Spectral Methods

If you have ever tried to compute a spectrum from unevenly spaced data—say, stock prices logged at random times, or astronomical observations interrup...