Matrix representation of Taylor’s formula for mappings in finite dimensional spaces

Author
P. S. Senio
Ivan Franko National University of Lviv, Lviv, Ukraine
Abstract
In this paper, the matrix representations of derivatives, differentials and Taylor’s formulas for functionals and mappings are presented. The behavior law of intermediate points in the formula’s remainder terms is found for shrinking the expansion interval of mapping to a point. This, in particular, allows one to analyze the local uncertainties in the remainder terms of Taylor’s formula and to develop and explore the new effective methods for solving systems of nonlinear algebraic equations.
Keywords
functional and mapping derivatives; functional and mapping differentials; Taylor’s formula for functionals and mappings; remainder terms of Taylor’s formula
DOI
doi:10.15330/ms.51.1.92-106
Reference
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Pages
92-106
Volume
51
Issue
1
Year
2019
Journal
Matematychni Studii
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