Numerical Solutions
From linear algebra: [A]-1[A][T]=[A]-1[C], [T]=[A]-1[C]
where [A]-1 is the inverse of matrix [A]. [T] is the solution vector.
- Matrix inversion requires cumbersome numerical computations and is not efficient if the order of the matrix is high (ᡂ)
- Gauss elimination method and other matrix solvers are usually available in many numerical solution package. For example, “Numerical Recipes” by Cambridge University Press or their web source at www.nr.com.
- For high order matrix, iterative methods are usually more efficient. The famous Jacobi & Gauss-Seidel iteration methods will be introduced in the following.