Ian Barrodale

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DESCRIPTION The algorithm calculates a Chebyshev (or l~) solution to an m X n overdetermined system of linear equations Ax = b, i.e. given equations the subroutine determines a vector x* = ['xl*, x~*,..., x,,*'] r which minimizes the maximum absolute value of the residuals (1) The algorithm can be used to solve the linear Chebyshev data fitting problem.(More)
When analyzing linear systems of equations, the most important indicator of potential instability is the condition number of the matrix. For a convolution matrix W formed from a series w (where Wij defines the stabirity of the deconvolution process. For the larger con-volution matrices commonly encountered in practice, direct computation of the condition(More)
1. INTRODUCTION Geographic Information Systems (GIS) provide well-developed tools for query, analysis and display of point, line, and polygon data, and there are well-developed communities that use these data types and rely heavily on GIS tools. Many meteorological datasets consist of combinations of time series and grids. Tools for query, analysis and(More)
DESCRIPTION Given any n × n system of linear equations A x = b (1) and a n u m b e r e, the algorithm calculates the solution x to (1), if ~ _< O, or an approximation solution x (k) satisfying I[b-A x (k) II~ < e, (2) if E > 0. Furthermore, if A appears to be singular, an approximate solution to (1) is still determined, although it does not satisfy (2). The(More)