Matrix representation of Taylor’s formula for mappings in finite dimensional spaces |
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Author |
senio.petro@gmail.com
Ivan Franko National University of Lviv,
Lviv, Ukraine
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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.
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Keywords |
functional and mapping derivatives; functional and mapping differentials; Taylor’s formula for
functionals and mappings; remainder terms of Taylor’s formula
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DOI |
doi:10.15330/ms.51.1.92-106
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Reference |
1. Kolmogorov A.N., Fomin S.V., Elements of the theory of functions and functional analysis. M.: Nauka,
1989. (in Russian)
2. Ortega J., Ranboldt V., Iterative methods for solving nonlinear systems of equations with many unknowns. M.: Mir, 1975. (in Russian) 3. Senio P.S., A new approach to the construction of interval methods for solving nonlinear equations, Visn. Lviv Univ., Ser. Mekh.-Mat., 31 (1989), 85–92. (in Ukranian) 4. Senio P.S., Interval methods for solving certain classes of deterministic problems, Visn. Lviv Univ., Ser. Prykladn. Mat. Inform., 7 (2003), 86–96. (in Ukranian) 5. Senio P.S., Two-sided approximation finding of a function based on mathematics of functional intervals. Proceedings of XXXII International Conference PDMU. Czech Republic. Prague. August 27-31, 2018, 146–154. 6. Ilin V.A., Sadovnichiy V.A., Sendov B.K., Mathematical Analysis. Beginner course. M.: MGU, 1985. (in Russian) 7. Schwartz L., Analysis, V.1, M.: Mir, 1972. (in Russian) 8. Zorich V.A., Mathematical Analysis II. Berlin-Heidelberg: Springer-Verlag, 2 ed., 2016. |
Pages |
92-106
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Volume |
51
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Issue |
1
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Year |
2019
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Journal |
Matematychni Studii
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Full text of paper | |
Table of content of issue |