Introduction to Computational Linear Algebra

16 Introduction to Computational Linear Algebra

To illustrate such situations, let us look respectively at the 3-point and 5-

point discretization of the Laplacian operator in 1 and 2 dimensions.

In the first case, with p grid points one gets a tridiagonal matrix of order

n = p with n

z

= 3n−2 non-zero entries. On the other hand, in a 2-dimensional

square grid of p ×p grid points and by numbering the nodes by rows, one gets

a matrix of order n = p

2

, in which every row has a maximum of 5 non-zero

entries. The non-zero entries are then located on 5 non-zero diagonals that

are not contiguous as in the tridiagonal case. Independently, the number n

z

of

non-zeros ...