Theory

This section provides the mathematical and algorithmic foundations of the Sparse SGWT library. It covers the definition of the graph Laplacian as a discrete operator, the analytical forms of spectral filters, the rational approximation of custom kernels via Vector Fitting, and the implementation details of the high-performance Cholesky-based solvers that enable scalable graph convolutions.

• Graph Laplacian
  • The Physics of the Weights
  • Derivation of the Delay Weight
  • Summary of Useful Weighting Schemes
• Analytical Filters
  • Low-Pass Spectral Graph Filter
  • High-Pass Spectral Graph Filter
  • Band-Pass Spectral Graph Filter
• Kernel Fitting
  • From Polynomials to Linear Solves