The generalization of Exercise 10.5.31 to an n × n grid results in an n2 × n2 matrix in block tridiagonal form

in which K is the tridiagonal n × n matrix with 4's on the main diagonal and - l's on the sub- and super-diagonal, while I denotes an n x n identity matrix. Use the known value of the Jacobi spectral radius "

[65], to design an SOR method to solve the linear system Au = f. Run your method on the cases n = 5 and f = e13 and n = 25 and f = e313 corresponding to a unit force at the center of the grid. How much faster is the convergence rate?

Transcribed Image Text:

K -I к -1 к -1 A = -I K -I