Relaxation, including the Gauss-Seidel and Jacobi methods.There are examples such as geodesy where there many more measurements than unknowns. Such a system is almost always overdetermined and has no exact solution. Each measurement is usually inaccurate and includes some amount of error. Since the measurements are not exact, it is not possible to obtain an exact solution to the system of linear equations methods such as Least squares can be used to compute a solution that best fits the overdetermined system. This least squares solution can often be used as a stand-in for an exact solution. Solving a system of linear equations has a complexity of at most O (n 3). At least n 2 operations are needed to solve a general system of n linear equations. The best algorithm known to date was developed by Don Coppersmith and Shmuel Winograd and dates from 1990. It has a complexity of n 2.376 Unfortunately, it is of little practical use. Using computers to solve systems of linear equations is used every day. For example, it is used in weather forecasting models.
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