Research map / Learning theory and algorithms / Sample complexity
Faster Eigenvector Computation via Shift-and-Invert Preconditioning
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use shift-and-invert preconditioning with SVRG linear-system solves | Offline top eigenvector computation · Offline Eigenvector Estimation | runtime: O\left(\left [\nnz(\bv{A}) + \frac{d \nrank(\bv{A})}{\mathrm{gap}^2}\right ] \cdot \left [\log \frac{1}{\epsilon} + \log | Helped |
| Accelerate the shift-and-invert solver | Offline top eigenvector computation when nnz(A) ≤ d stable-rank(A)/gap² · Offline Eigenvector Estimation | runtime: O\left(\left [\frac{\nnz(\bv{A})^{3/4}(d \nrank(\bv{A}))^{1/4}}{\sqrt{\mathrm{gap}}}\right ] \cdot \left[\log \frac{d}{\ | Helped |
| Refine an O(gap) initial estimate using streaming SVRG | Online top eigenvector estimation · Online Eigenvector Estimation | sample complexity: O\left ( \frac{d}{\mathrm{gap}^2 \epsilon} \right ) | Helped |
| Use shift-and-invert instead of the power method | Top eigenvector computation · Offline Eigenvector Estimation | iterations: O (\log(d/\epsilon)/\mathrm{gap} ) -> O (\log (d/\epsilon) ) | Helped |
Closest papers by meaning
- Gradient Descent Meets Shift-and-Invert Preconditioning for Eigenvector Computation (NeurIPS 2018 · similarity 0.89)
- Exploiting Numerical Sparsity for Efficient Learning : Faster Eigenvector Computation and Regression (NeurIPS 2018 · similarity 0.89)
- Approximating the Top Eigenvector in Random Order Streams (NeurIPS 2024 · similarity 0.87)
- Fast and Stable Gradient Approximation for Bilinear Forms of Hermitian Matrix Functions (NeurIPS 2026 · similarity 0.83)
- Explicit Eigenvalue Regularization Improves Sharpness-Aware Minimization (NeurIPS 2024 · similarity 0.83)
- Nonlinear Laplacians: Tunable principal component analysis under directional prior information (NeurIPS 2025 · similarity 0.83)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.