Preliminary remarks on multigrid methods for circulant matrices

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1988, Issue , 2001, Pages 152-159

  Capizzano, Stefano Serra ^a   Possio, Cristina Tablino ^b  

^a UNIVERSITY OF FLORENCE   (Italy)

^b UNIVERSITY OF MILANO BICOCCA   (Italy)

Author keywords

Circulant matrices; Two grid and multigrid iterations

Indexed keywords

FAST FOURIER TRANSFORMS; IMAGE RECONSTRUCTION; LINEAR SYSTEMS; NUMERICAL ANALYSIS; OPTICAL TRANSFER FUNCTION;

ARITHMETIC OPERATIONS; CIRCULANT MATRIX; MULTIGRID APPROACH; MULTIGRID TECHNIQUE; NUMERICAL EXPERIMENTS; PERIODIC BOUNDARY CONDITIONS; PRECONDITIONED CONJUGATE GRADIENT; TWO-GRID AND MULTIGRID ITERATIONS;

MATRIX ALGEBRA;

EID: 23044526698     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-45262-1_19     Document Type: Conference Paper

References (20)

1. D. Bini and M. Capovani, “Spectral and computational properties of band symmetric Toeplitz matrices”, Linear Algebra Appl., 52/53 (1983), pp. 99–125.
2. R. H. Chan and T. F. Chan, “Circulant preconditioners for elliptic problems”, J. Numer. Linear Algebra Appl., 1 (1992), pp. 77–101.
3. R. H. Chan, Q. Chang and H. Sun, “Multigrid method for ill-conditioned symmetric Toeplitz systems”, SIAM J. Sci. Comp., 19-2 (1998), pp. 516–529.
4. R. H. Chan and M. Ng, “Conjugate gradient methods for Toeplitz systems”, SIAM Rev., 38 (1996), pp. 427–482.
5. R. H. Chan and G. Strang, “Toeplitz equations by conjugate gradients with circulant preconditioner”, SIAM J. Sci. Stat. Comp., 10 (1989), pp. 104–119.
6. T. F. Chan, “An optimal circulant preconditioner for Toeplitz systems”, SIAM J. Sci. Stat. Comp., 9 (1988), pp. 766–771.
7. F. Di Benedetto and S. Serra Capizzano, “A unifying approach to abstract matrix algebra preconditioning”, Numer. Math., 82-1 (1999), pp. 117–142.
8. G. Fiorentino and S. Serra, “Multigrid methods for Toeplitz matrices”, Calcolo, 28 (1991), pp. 283–305.
9. G. Fiorentino and S. Serra, “Multigrid methods for symmetric positive definite block Toeplitz matrices with nonnegative generating functions”, SIAM J. Sci. Comp., 17-4 (1996), pp. 1068–1081.
10. W. Hackbusch, Multigrid Methods and Applications. Springer Verlag, Berlin, 1985.
11. S. Holmgren and K. Otto, “Iterative solution methods and preconditioners for block tridiagonal systems of equations”, SIAM J. Matrix Anal. Appl., 13 (1992), pp. 863–886.
12. S. Holmgren and K. Otto, “Semicirculant preconditioners for first order partial differential equations”, SIAM J. Sci. Comput., 15 (1994), pp. 385–407.
13. T. Huckle, “Multigrid preconditioning and Toeplitz matrices”, private communication.
14. X. Q. Jin and R. Chan, “Circulant preconditioners for second order hyperbolic equations”, BIT, 32 (1992), pp. 650–664.
15. I. Lirkov, S. Margenov and P. Vassilevsky, “Circulant block factorization for elliptic problems”, Computing, 53 (1994), pp. 59–74.
16. S. Serra Capizzano and C. Tablino Possio, “Spectral and structural analysis of high precision Finite Difference matrices for Elliptic Operators”, Linear Algebra Appl., 293 (1999), pp. 85–131.
17. S. Serra, “A Korovkin - type Theory for finite Toeplitz operators via matrix algebras”, Numer. Math., 82-1 (1999), pp. 117–142.
18. S. Serra Capizzano and C. Tablino Possio, “Multigrid methods for multilevel circulant matrices”, manuscript, (2000).
19. E. Tyrtyshnikov, “Circulant preconditioners with unbounded inverses”, Linear Algebra Appl., 216 (1995), pp. 1–23.
20. E. Tyrtyshnikov, “A unifying approach to some old and new theorems on distribution and clustering”, Linear Algebra Appl., 232 (1996), pp. 1–43.