By R. Schmidt
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Extra resources for Advances in Nonlinear Parameter Optimization
Nonlinear Parameter Estimation New York and London: Academic Press (1974). : Applied Nonlinear Programming New York: McGraw-Hill, Inc. (1972).  Pierre. : Optimization Theory with Applications New York: J. Wiley & Sons, Inc. (1969).  v. : EinfUhrung in die H~here Mathematik Zweiter Band, 14. Auflage Stuttgart: S, Hirzel Verlag (1974). : Introduction to Nonlinear Optimization New York: Elsevier North-Holland, Inc. (1978). : Unified Approach to Quadratically Convergent Algorithms for Function Minimization J.
K) at the point x_k becomes minimal i f we only add one further vector to the already selected vectors. By adding further linearly independent vectors we approach to as small a value as possible of the slope of the function Q(x3+ eLk) at the point kx which is given by eq. 1/2).
3/12) we state that the matrix ~0 is a lxl-matrixt that means i t is a scalar. This scalar shall be denotated by a~. The index l is chosen in 48 order to remember that the scalar a~ refers to 1 selected vectors ~ , . . , _d~. To guarantee the existence of the reciproke of a~ the scalar a~ has to be different from zero. 3113) nknk+ is an orBy inspecting eqs. 2/23) we recognize that the matrix ~l=l thogonal projector because i t is idempotent and symmetric. Because of eq. ~) and -I+1 = ~ + i + ~I+1 with ~1+1 E R k~ E R(D~)~ .