Matrix solvers & numerical linear algebra
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At each step of many of the iterative algorithms we've discussed — particularly the Gradient Algorithm and Newton-Raphson methods — the core computational task often boils down to solving a large system of simultaneous linear equations. Even if the original network equations are non-linear, these methods linearize them in some way during each iteration.
This section will highlight the absolutely critical role that numerical linear algebra and efficient matrix solvers play in making modern hydraulic modeling feasible. The systems of equations generated can involve thousands, or even tens or hundreds of thousands, of variables for real-world networks.
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