4 Direct Methods for Solving Linear Systems

Linear systems are the commonest problem of scientific computation; most of the later methods of this course (interpolation, splines, least squares, implicit methods for differential equations) end by solving one. This section treats direct methods, which give the exact solution in a finite number of steps if the arithmetic is exact. Their accuracy in finite-digit arithmetic depends on how they are organized, and the main practical lesson is the need for pivoting.

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