# Approximations and error bounds for computing the inverse mapping

Lucas Jódar; Enrique Ponsoda; G. Rodríguez Sánchez

Applications of Mathematics (1997)

- Volume: 42, Issue: 2, page 99-110
- ISSN: 0862-7940

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topJódar, Lucas, Ponsoda, Enrique, and Rodríguez Sánchez, G.. "Approximations and error bounds for computing the inverse mapping." Applications of Mathematics 42.2 (1997): 99-110. <http://eudml.org/doc/32971>.

@article{Jódar1997,

abstract = {In this paper we propose a procedure to construct approximations of the inverse of a class of $\{\mathcal \{C\}\}^\{m\}$ differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.},

author = {Jódar, Lucas, Ponsoda, Enrique, Rodríguez Sánchez, G.},

journal = {Applications of Mathematics},

keywords = {approximations; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example},

language = {eng},

number = {2},

pages = {99-110},

publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},

title = {Approximations and error bounds for computing the inverse mapping},

url = {http://eudml.org/doc/32971},

volume = {42},

year = {1997},

}

TY - JOUR

AU - Jódar, Lucas

AU - Ponsoda, Enrique

AU - Rodríguez Sánchez, G.

TI - Approximations and error bounds for computing the inverse mapping

JO - Applications of Mathematics

PY - 1997

PB - Institute of Mathematics, Academy of Sciences of the Czech Republic

VL - 42

IS - 2

SP - 99

EP - 110

AB - In this paper we propose a procedure to construct approximations of the inverse of a class of ${\mathcal {C}}^{m}$ differentiable mappings. First of all we determine in terms of the data a neighbourhood where the inverse mapping is well defined. Then it is proved that the theoretical inverse can be expressed in terms of the solution of a differential equation depending on parameters. Finally, using one-step matrix methods we construct approximate inverse mappings of a prescribed accuracy.

LA - eng

KW - approximations; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example; inverse mapping; error bounds; Banach space; matrix differential equations; one-step-method; numerical example

UR - http://eudml.org/doc/32971

ER -

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