The paper analyzes a two-grid and a multigrid method for matrices belonging to the DCT-III algebra and generated by a polynomial symbol. The aim is to prove that the convergence rate of the considered multigrid method (V-cycle) is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are considered to illustrate the claimed convergence properties.
TABLINO POSSIO, C. (2010). V-cycle optimal convergence for DCT-III matrices. In D.A. Bini, V. Mehrmann, V. Olshevsky, E.E. Tyrtyshnikov, M. VanBarel (a cura di), Numerical Methods for Structured Matrices and Applications: The Georg Heinig Memorial Volume (pp. 377-396). Birkhäuser [10.1007/978-3-7643-8996-3_17].
V-cycle optimal convergence for DCT-III matrices
TABLINO POSSIO, CRISTINA
2010
Abstract
The paper analyzes a two-grid and a multigrid method for matrices belonging to the DCT-III algebra and generated by a polynomial symbol. The aim is to prove that the convergence rate of the considered multigrid method (V-cycle) is constant independent of the size of the given matrix. Numerical examples from differential and integral equations are considered to illustrate the claimed convergence properties.
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