Name
Abstract | ||
|---|---|---|
A generalization of the cyclic Jacobi algorithm is proposed that works in an arbitrary compact Lie algebra. This allows, in particular, a unified treatment of Jacobi algorithms on different classes of matrices, e.g., skew-symmetric or skew-Hermitian Hamiltonian matrices. Wildberger has established global, linear convergence of the algorithm for the classical Jacobi method on compact Lie algebras. Here we prove local quadratic convergence for general cyclic Jacobi schemes. |
Year | DOI | Venue |
|---|---|---|
2004 | 10.1137/S0895479802420069 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
compact lie algebra,linear convergence,classical jacobi method,local quadratic convergence,skew-hermitian hamiltonian matrix,jacobi algorithm,compact lie algebras,different class,arbitrary compact lie algebra,cyclic jacobi algorithm,general cyclic jacobi scheme,cost function,generalized eigenvalue problem,optimization,numerical linear algebra,normal matrices,quadratic convergence,eigenvalues,system theory,quadratic programming,parameter estimation,sum of squares,jacobi method,symmetric matrices,hermitian matrices,lie algebra,parallel computer | Jacobi identity,Jacobi rotation,Jacobi method,Algebra,Mathematical analysis,Jacobi operator,Jacobi eigenvalue algorithm,Algorithm,Compact Lie algebra,Adjoint representation of a Lie algebra,Lie conformal algebra,Mathematics | Journal |
Volume | Issue | ISSN |
26 | 1 | 0895-4798 |
Citations | PageRank | References |
1 | 0.37 | 2 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| M. Kleinsteuber | 1 | 24 | 3.33 |
| Uwe Helmke | 2 | 337 | 42.53 |
| Knut Hueper | 3 | 7 | 0.92 |