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Linear Algebra

Linear Algebra

This section introduces methods to solve systems of linear equations, expressed in terms of a matrix equation, Ax=b, in which the vector, x, is to be determined. The Gauss-Jordan Elimination method is one in which the inverse of the matrix, A, is calculated. If the inverse is not needed, then using Gaussian Elimination with backsubstitution is preferred, as it is about 3 times faster. For repeated solutions to problems that involve the same matrix, but various right hand sides, the LU decomposition method is recommended.

Iterative improvements to the solution, dealing with singular problems, and methods for sparse matrices are briefly discussed.

The exercise is an application of these methods to solve a general resistor divider network.

Reference:

Numerical Recipies, chapter 2.

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