Chapter 2: Q2.5-32Q (page 93)
The band matrixAshown below can be used to estimate
the unsteady conduction of heat in a rod when the temperatures at points
The constantCin the matrix depends on the physical nature
of the rod, the distance
and the length of time
measurements. Suppose that for
in
rod are maintained at
the equation
- Find the LU factorization ofAwhen
. A matrix
such as Awith three nonzero diagonals is called a tridiagonal matrix. The Land Ufactors are bidiagonal matrices.
- Suppose
and . Use the
LU factorization of Ato find the temperature distributions , , , and .
Short Answer
- The LU factorizations are
2. The temperature distributions are