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A new algorithm for the Chebyshev solution of overdetermined linear systems

Author: Paul T. Boggs
Journal: Math. Comp. 28 (1974), 203-217
MSC: Primary 65F20
MathSciNet review: 0334482
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Abstract: Let $ x(p)$ be the point which minimizes the residual of a linear system in the $ {l_p}$ norm. It is known that under certain conditions $ x(p) \to {x^\ast}$, the Chebyshev or $ {l_\infty }$ solution, as $ p \to \infty $. A differential equation describing $ x(p)$ is derived from which an iterative scheme is devised. A convergence analysis is given and numerical results are presented.

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Keywords: Pólya algorithm, $ {l_p}$ solutions, differential equation for $ {l_p}$ solutions, stable integration techniques
Article copyright: © Copyright 1974 American Mathematical Society