Numerical Linear Algebra

• Stabilizing Gradients for Deep Neural Networks via Efficient SVD Parameterization (pdf, arXiv, software)
  J. Zhang, Q. Lei, I. Dhillon.
  In International Conference on Machine Learning (ICML), pp. 5801–5809, July 2018.
• 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.
• On a Zero-Finding Problem involving the Matrix Exponential (pdf, software)
  M. Sustik, I. Dhillon.
  SIAM Journal of Matrix Analysis and Applications (SIMAX) 33(4), pp. 1237-1249, 2012.
• Clustered Low Rank Approximation of Graphs in Information Science Applications (pdf, software)
  B. Savas, I. Dhillon.
  In SIAM International Conference on Data Mining (SDM), pp. 164-175, April 2011.
• 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.
• Computation of the Singular Value Decomposition (pdf, software)
  A. Cline, I. Dhillon.
  Handbook of Linear Algebra, pp. 45-1–45-13, January 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.
• Generalized Finite Algorithms for Constructing Hermitian Matrices with Prescribed Diagonal and Spectrum (pdf, software)
  I. Dhillon, R. Jr., M. Sustik, J. Tropp.
  SIAM Journal of Matrix Analysis and Applications (SIMAX) 27(1), pp. 61-71, June 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.
• Reliable computation of the Condition Number of a Tridiagonal Matrix in O(n) Time (pdf, software)
  I. Dhillon.
  SIAM Journal of Matrix Analysis and Applications (SIMAX) 19(3), pp. 776-796, July 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.
• ScaLAPACK: A Linear Algebra Library for Message-Passing Computers (pdf, software)
  L. Blackford, J. Choi, A. Cleary, E. D’Azevedo, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, R. Whaley.
  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.
• ScaLAPACK Users’ Guide (pdf, software)
  L. Blackford, J. Choi, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, R. Whaley.
  ScaLAPACK Users’ Guide, 1997.
• ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers – Design Issues and Performance (pdf, software)
  J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R. Whaley.
  Computer Physics Communications 97, pp. 1-15, August 1996.
• ScaLAPACK: A Portable Linear Algebra Library for Distributed Memory Computers – Design Issues and Performance (pdf, software)
  L. Blackford, J. Choi, A. Cleary, J. Demmel, I. Dhillon, J. Dongarra, S. Hammarling, G. Henry, A. Petitet, K. Stanley, D. Walker, R. Whaley.
  In Supercomputing (SC), 1996.
• 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.
• Installation Guide for ScaLAPACK (pdf, software)
  J. Choi, J. Demmel, I. Dhillon, J. Dongarra, S. Ostrouchov, A. Petitet, K. Stanley, D. Walker, R. Whaley.
  University of Tennessee Computer Science Technical Report (UT-CS-95-280) UT-CS-95-280, March 1995.
  (updated August 31, 2001 (version 1.7) — also available as LAPACK Working Note 93)
• Efficient Computation of the Singular Value Decomposition with Applications to Least Squares Problems (pdf, software)
  M. Gu, J. Demmel, I. Dhillon.
  Technical Report LBL-36201, October 1994.