ISSN:
1420-9039
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Summary The paper begins with a short description of the theory of overdetermined linear systems (Ausgleichsrechnung), using the notation of matrix-calculus. The solution of such systems by means of relaxation-methods is then discussed. In particular a broad description of the method of conjugate gradients is given. The algorithm avoids the use of the matrix of the normal equations. Lastly the application of the ‘method of the hypercircle’, developed bySynge and others, to this problem of linear algebra is studied, with the aim of finding upper and lower bounds for the sum of the square residuals — this sum being a minimum for the solution of the system. To get these bounds, we need approximate solutions obtained as intermediate values in an iterative process.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01600605
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