Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration *

@inproceedings{BankSharpEF,
  title={Sharp Estimates for Multigrid Rates of Convergence with General Smoothing and Acceleration *},
  author={Randolph E. Bank and C. C. Douglas and Ma{\^i}tre and Musy and Van Rosendale}
}
In this paper, we prove the convergence of the multilevel iterative method for solving linear equations that arise from elliptic partial differential equations. Our theory is presented entirely in terms of the generalized condition number K of the matrix A and the smoothing matrix B. This leads to a completely algebraic analysis of the method as an iterative technique for solving linear equations; the properties of the elliptic equation and discretization procedure enter only when we seek to… CONTINUE READING
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BAKHVALOV , On the convergence of a relaxation method under natural constraints on an elliptic operator

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