Solving Sets of Equations

• Solving sets of linear equations and eigenvalue problems are the most frequently used numerical procedures when real-world situations are modelled.
• Analytical solution may be feasible when the number of unknowns is small.
• However, computers outperforms to solve large systems of linear equations such as with 100 unknowns in a reasonable time.

1. Matrices and Vectors. Reviews concepts of matrices and vectors in preparation for their use.
2. Elimination Methods. Describes classical methods that change a system of equations to forms that allow getting the solution by back-substitution and shows how the errors of the solution can be minimized.
3. The Inverse of a Matrix. Shows how an important derivative of a matrix, its inverse, can be computed. It shows when a matrix cannot be inverted and tells of situations where no unique solution exists to a system of equations.
4. Iterative Methods. It is described how a linear system can be solved in an entirely different way, by beginning with an initial estimate of the solution.