Research map / Learning theory and algorithms / Matrix and tensor methods
Analysis of stochastic Lanczos quadrature for spectrum approximation
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use independent uniform unit-sphere vectors and average their weighted CESM estimates | SLQ · Symmetric matrix spectrum approximation | Wasserstein distance: t I[\mathbf{A}] | Helped |
| Increase the number of Lanczos iterations to k | SLQ Gaussian quadrature · Weighted CESM approximation | Wasserstein distance: 12 I[\mathbf{A}] (2k-1)^{-1} | Helped |
| Increase the number of independent uniform unit-sphere samples | Weighted CESM estimator · Fixed threshold x | absolute CESM estimation error: 2 \exp\left( - n_{\textup{v}} (n+2) t^2 \right) | Helped |
| Use fewer than (8t)^{-1} matrix-vector products | SLQ · A constructed symmetric matrix | Wasserstein distance: > t I[\mathbf{A}] | Hurt |
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