Abstract
We introduce a class of Multigrid methods for solving banded, symmetric Toeplitz systems Ax=b. We use a, special choice of the projection operator whose coefficients simply depend on some spectral properties of A. This choice leads to an iterative Multigrid method with convergence rate smaller than 1 independent of the condition number K2(A) and of the dimension of the matrix. In the second part the B0 class is introduced: this class, of Toeplitz matrices contains the linear space generated by the matrices arising from the finite differences discretization of the differential operators Open image in new window , m∈N +. To sum up we present an adaptive algorithm which has a input the coefficients of A and return an iterative Multigrid method with convergence speed independent of the mesh spacing h and with an asymptotical cost of O(n).
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
