What Are the Limitations of Real-Space Methods on a Single Fine Grid

What Are the Limitations of Real-Space Methods on a Single Fine Grid  

If we iterate toward the solution as discussed above, the residual decreases quickly at first, but then the convergence slows considerably. This 

The update or relaxation Eq. [25] can be written as a matrix equation. We are interested in the mathematical properties of the update matrix, so we will calculate the eigenvalues of that matrix. Let the update matrix act upon a plane wave with wavevector k. Then our eigenvalue equation is 

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