The eigenvalues of preconditioned matrices for linear multistep formulas in boundary value form

Numerical Linear Algebra with Applications

Volumn 12, Issue 2-3, 2005, Pages 315-325

  Bertaccini, Daniele ^a   Wen, Youwei ^b   Ng, Michael K ^c  

^a SAPIENZA UNIVERSITY OF ROME   (Italy)

^b GUANGDONG UNIVERSITY OF TECHNOLOGY   (China)

^c UNIVERSITY OF HONG KONG   (Hong Kong)

Author keywords

Circulant matrices; Eigenvalues; Linear multistep formulas in bv form; Non symmetric Toeplitz matrices

Indexed keywords

EID: 20744441827     PISSN: 10705325     EISSN: None     Source Type: Journal    
DOI: 10.1002/nla.419     Document Type: Article

References (7)

1. Axelsson AOH, Verwer JG. Boundary value techniques for initial value problems in ordinary differential equations. Mathematics of Computation 1985; 45:153-171.
2. Bertaccini D. A circulant preconditioner for the systems of LMF-based ODE code. SIAM Journal on Scientific Computing 2000; 22(3):767-786.
3. Bertaccini D. Reliable preconditioned iterative linear solvers for some numerical integrators. Numerical Linear Algebra with Application 2001; 8(2):111-125.
4. Chan RH, Ng MK, Jin XQ. Circulant preconditioners for solving ordinary differential equations. IMA Journal of Numerical Analysis 2001; 21:451-462.
5. Bertaccini D, Ng MK. The convergence rate of block preconditioned systems arising from LMF-based ODE codes. BIT 2001; 41(3):433-450.
6. Bertaccini D. The spectrum of circulant-like preconditioners for some general linear multistep formulas for linear boundary value problems. SIAM Journal on Numerical Analysis 2002; 40(5):1798-1822.
7. Otto K. Analysis of preconditioners for hyperbolic partial differential equations. SIAM Journal on Numerical Analysis 1996; 33(6):2131-2165.