Multigrid Methods - Finite Elements: Theory, Fast Solvers, and Applications in Elasticity Theory - page 236

1.10 Write Algorithm 1.7 as a formal procedure MGM (A ,b ,x ,k ) in PASCAL
or some other programming language.

1.11 What is the (one-dimensional) stencil of the restriction operator with the
matrix representation (1.14)?

1.12 Dividing the squares into triangles in the model Example II.4.3 results in
an unsymmetric stencil for the prolongation in (1.15). The symmetric form

< ?

1
4

1
2

1
4

> A

1
2

1
2

p = 1 ( 1 . 17 )

1
4

1
2

1
4

∗

appears more natural. What are the stencils for the restriction operators which arise
from (1.15) and (1.17) via the matrix equation r = p t ?