Eigenvalue computation in the 20th century

By Gene H. Golub, Henk A. van der Vorst. 2000

447 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Numerical Analysis, Numerical Methods & Scientific Computing

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. Tetsuya Sakurai
2. Fernando De la Torre
3. Liqiang Nie
4. Lawrence Carin
5. Hiroshi Sugiura
6. Shin Ishii
7. Changyou Chen
8. Ken Nakae

In Numerical Analysis

1. Tetsuya Sakurai
2. Fernando De la Torre
3. Lawrence Carin
4. Hiroshi Sugiura
5. Shin Ishii
6. Changyou Chen
7. Ken Nakae
8. Toshiki Kataoka

In Numerical Methods & Scientific Computing

1. Fernando De la Torre
2. Tetsuya Sakurai
3. Lawrence Carin
4. Hiroshi Sugiura
5. Shin Ishii
6. Changyou Chen
7. Ken Nakae
8. Toshiki Kataoka

Citations in the corpus

• Large Scale GAN Training for High Fidelity Natural Image Synthesis (2018, methodology): “They can be efficiently computed using the Alrnoldi iteration method (Golub & der Vorst, 2000), which extends the power iteration method, used in Miyato et al. (2018), to estimation of additional singular vectors and values.”
• Spectral Normalization for Generative Adversarial Networks (2018, methodology): “Instead, we can use the power iteration method to estimate σ ( W ) (Golub & Van der Vorst, 2000; Yoshida & Miyato, 2017).”
• Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning (2017, methodology): “We resolve this issue with the approximation via a power iteration method [8] and finite difference method.”
• Distributional Smoothing with Virtual Adversarial Training (2015, methodology): “We therefore resort to power iteration method (Golub & Van der Vorst, 2000) and finite difference method to approximate r v - adv .”
• A Framework for Robust Subspace Learning (2003, background): “mathematics ( Golub and van der Vorst, 2000; Parlett, 1980).”
• Second-Order Adversarial Attack and Certifiable Robustness (2018, methodology): “(2017) Power iteration method Golub & Van der Vorst (2001) allows one to compute the dominant eigenvector r of a matrix H .”
• Lipschitz Continuity Guided Knowledge Distillation (2021, methodology): “Instead of using SVD, we utilize power iteration method [9, 46, 29] to approximate the spectral norm of the targeted matrix with a small trade-off of accuracy, as presented in Algorithm 1.”
• Critical Eigenvalues Tracing for Power System Analysis via Continuation of Invariant Subspaces and Projected Arnoldi Method (2007, methodology): “Several variants of the Arnoldi method exist to improve convergence properties such as the deflated Arnoldi method and the implicitly restarted Arnoldi method [1]–[3].”
• Integro: Leveraging Victim Prediction for Robust Fake Account Detection in OSNs (2015, methodology): “Íntegro utilizes the power iteration method to efficiently compute trust values [49].”
• A projection method for generalized eigenvalue problems using numerical integration (2003, methodology): “A comprehensive report on computational methods for eigenvalue problems was given by Golub and van der Vorst [8].”