Scaling by Binormalization

  title={Scaling by Binormalization},
  author={Oren E. Livne and Gene H. Golub},
  journal={Numerical Algorithms},
We present an iterative algorithm (BIN) for scaling all the rows and columns of a real symmetric matrix to unit 2-norm. We study the theoretical convergence properties and its relation to optimal conditioning. Numerical experiments show that BIN requires 2–4 matrix–vector multiplications to obtain an adequate scaling, and in many cases significantly reduces the condition number, more than other scaling algorithms. We present generalizations to complex, nonsymmetric and rectangular matrices. 


Publications citing this paper.
Showing 1-10 of 23 extracted citations


Publications referenced by this paper.
Showing 1-10 of 23 references

Condition numbers and equilibration of matrices

  • A. van der Sluis
  • Num. Math.,
  • 1969
Highly Influential
7 Excerpts

On best conditioned matrices

  • G. E. Forsythe, E. G. Straus
  • Proc. Amer. Math. Soc.,
  • 1955
Highly Influential
8 Excerpts

Multigrid solvers and multilevel optimization strategies

  • A. Brandt, D. Ron
  • In Multilevel Optimization and VLSICAD (J. Cong…
  • 2002
1 Excerpt

Multiscale scientific computation: review

  • A. Brandt
  • Multiscale and Multiresolution Methods: Theory…
  • 2001

Matrix Iterative Analysis

  • R. S. Varga
  • 2000


  • U. Trottenberg, C. W. Oosterlee, A. Schüller
  • 2000

Multiscale Eigenbasis Algorithms

  • O. E. Livne
  • Weizmann Institute of Science, Rehovot,
  • 2000

Matrix Algorithms, Volume I: Basic Decompositions

  • G. W. Stewart
  • SIAM, Philadelphia,
  • 1998

Introduction to Matrix Analysis

  • R. B. Bellman
  • SIAM, Philadelphia,
  • 1997

Introduction to the Numerical Solution of Markov Chains

  • W. J. Stewart
  • 1994
1 Excerpt

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