Summary
The linear approximation procedure known as stochastic approximation (see [2, 4]) has strong connections to matrix-methods in summability-theory. The results in [2] can be derived directly from the Toeplitz-Lemma as was shown in [6, 7]. In this paper we give an analogy of the Toeplitz-Lemma with operators and as application a general multidimensional stochastic approximation procedure.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Anderson TW, Das Gupta S (1963) Some inequalities on characteristic roots of matrices. Biometrika 50:522–524
Blum JR (1954) Approximation methods which converge with probability one. Ann Math Stat 25:382–386
Mercer J (1907) On the limit of real variants. London MS Proc (2)5:206–224
Robbins H, Monro S (1951) A stochastic approximation method. Ann Math Stat 22:400–407
Roy SN (1954) A useful theorem in matrix-theory. Proc Am Math Soc 5:635–638
Vogel W (1984) Ein Mercer-Satz mit Anwendungen auf die Theorie der stochastischen Approximation. SFB-preprint Nr 686, Bonn
Vogel W (1986) Sequential approximation with errors. SFB-preprint Nr 804, Bonn
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Vogel, W. (1987). Sequential Approximation with Errors in Normed Linear Spaces. In: Opitz, O., Rauhut, B. (eds) Ökonomie und Mathematik. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72672-9_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-72672-9_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-72673-6
Online ISBN: 978-3-642-72672-9
eBook Packages: Springer Book Archive