Eigenvalue Decomposition

• Coordinate-wise Power Method (pdf, software, code)
  Q. Lei, K. Zhong, I. Dhillon.
  To appear in Neural Information Processing Systems (NIPS), December 2016.
• Multi-Scale Spectral Decomposition of Massive Graphs (pdf, software)
  S. Si, D. Shin, I. Dhillon, B. Parlett.
  In Neural Information Processing Systems (NIPS), pp. 2798-2806, December 2014.
• The Design and Implementation of the MRRR Algorithm (pdf, software)
  I. Dhillon, B. Parlett, C. Vömel.
  ACM Transactions on Mathematical Software 32(4), pp. 533-560, December 2006.
• Glued Matrices and the MRRR Algorithm (pdf, software)
  I. Dhillon, B. Parlett, C. Vömel.
  SIAM Journal on Scientific Computing 27(2), pp. 496-510, October 2005.
• A Parallel Eigensolver for Dense Symmetric Matrices based on Multiple Relatively Robust Representations (pdf, software)
  P. Bientinesi, I. Dhillon, R. Geijn.
  SIAM Journal on Scientific Computing 27(1), pp. 43-66, September 2005.
• Multiple Representations to Compute Orthogonal Eigenvectors of Symmetric Tridiagonal Matrices (pdf, software)
  I. Dhillon, B. Parlett.
  Linear Algebra and its Applications 387, pp. 1-28, August 2004.
• Orthogonal Eigenvectors and Relative Gaps (pdf, software)
  I. Dhillon, B. Parlett.
  SIAM Journal of Matrix Analysis and Applications (SIMAX) , pp. 858-899, March 2004.
• Inner deflation of Symmetric, Tridiagonal Matrices (pdf, software)
  I. Dhillon, A. Malyshev.
  Linear Algebra and its Applications 358(1), pp. 139-144, January 2003.
• Relatively Robust Representations for Symmetric Tridiagonals (pdf, software)
  B. Parlett, I. Dhillon.
  Linear Algebra and its Applications 309, pp. 121-151, November 2000.
• Current Inverse Iteration Software can Fail (pdf, software)
  I. Dhillon.
  BIT Numerical Mathematics 38(4), pp. 685-704, December 1998.
• A New O(N^2) Algorithm for the Symmetric Tridiagonal Eigenvalue/Eigenvector Problem (pdf, software)
  I. Dhillon.
  Ph.D. Thesis, May 1997.
  (Also appears as UCB Tech. Report No. UCB//CSD-97-971)
• Application of a New Algorithm for the Symmetric Eigenproblem to Computational Quantum Chemistry (pdf, software)
  I. Dhillon, G. Fann, B. Parlett.
  In SIAM Conference on Parallel Processing for Scientific Computing, March 1997.
• Fernando’s Solution to Wilkinson’s Problem: An Application of Double Factorization (pdf, software)
  B. Parlett, I. Dhillon.
  Linear Algebra and its Applications, pp. 247-279, 1997.
• On the Correctness of Some Bisection-like Parallel Algorithms in Floating Point Arithmetic (pdf, software)
  J. Demmel, I. Dhillon, H. Ren.
  Electronic Transactions of Numerical Analysis (ETNA), December 1995.