Zero-preserving iso-spectral flows based on parallel sums

Linear Algebra and Its Applications

Volumn 421, Issue 1, 2007, Pages 69-84

  Driessel, Kenneth R ^a   Gerisch, Alf ^b  

^a Department of Environmental and Radiological Health Sciences   (United States)

^b MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

Differential geometry; Double bracket flow; Dynamical system; Eigenvalues; Group action; Harmonic mean; Iso spectral flow; Orbit; Ordinary differential equation; Parallel sum; Projection; QR algorithm; Quasi projection; Sparse matrix; Toda flow; Vector field

Indexed keywords

ALGORITHMS; MATRIX ALGEBRA; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS;

DIFFERENTIAL GEOMETRY; DOUBLE BRACKET FLOW; DYNAMICAL SYSTEMS; GROUP ACTION; HARMONIC MEAN; ISO SPECTRAL FLOW; PARALLEL SUM; SPARSE MATRIX; TODA FLOW; VECTOR FIELD;

MATHEMATICAL TRANSFORMATIONS;

EID: 33845669119     PISSN: 00243795     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.laa.2006.07.013     Document Type: Article

References (13)

1. Anderson Jr. W.N., and Duffin R.J. Series and parallel addition of matrices. J. Math. Anal. Appl. 26 (1969) 576-594
2. Anderson Jr. W.N. Shorted operators. SIAM J. Appl. Math. 20 (1971) 520-525
3. Anderson Jr. W.N., and Schreiber M. The infimum of two projections. Acta Sci. Math. 33 (1972) 165-168
4. Anderson Jr. W.N., and Trapp G.E. Shorted operators II. SIAM J. Appl. Math. 28 (1975) 60-71
5. Bellman R. Introduction to Matrix Analysis (1970), McGraw-Hill
6. Curtis M.L. Matrix Groups (1984), Springer-Verlag
7. Driessel K.R. Computing canonical forms using flows. Linear Algebra Appl. 379 (2004) 353-379
8. K.R. Driessel, A. Gerisch, Zero-preserving iso-spectral flows based on parallel sums, 2006. math.GM/0605243. Available from: .
9. Fasino D. Iso-spectral flows on displacement structured matrix spaces. In: Bini D., Tyrtyshnikov E., and Yalamov P. (Eds). Structured Matrices: Recent Developments in Theory and Computation (2001), Nova Science Publisher Inc.
10. Hirsch M.W., Smale S., and Devaney R.L. Differential Equations. second ed. Dynamical Systems & An Introduction to Chaos (2004), Elsevier
11. Kubo K., and Ando T. Means of positive linear operators. Mathematische Annalen 246 (1980) 205-224
12. Lawson C., and Hanson R. Solving Least Squares Problems (1974), Prentice-Hall, Inc.
13. Warner F.W. Foundations of Differential Manifolds and Lie Groups (1983), Springer-Verlag