| Title:
|
Approximations and error bounds for computing the inverse mapping (English) |
| Author:
|
Jódar, L. |
| Author:
|
Ponsoda, E. |
| Author:
|
Rodríguez, G. |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
42 |
| Issue:
|
2 |
| Year:
|
1997 |
| Pages:
|
99-110 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
approximations |
| Keyword:
|
inverse mapping |
| Keyword:
|
error bounds |
| Keyword:
|
Banach space |
| Keyword:
|
matrix differential equations |
| Keyword:
|
one-step-method |
| Keyword:
|
numerical example |
| MSC:
|
15A24 |
| MSC:
|
26B10 |
| MSC:
|
34A45 |
| MSC:
|
34G20 |
| MSC:
|
65D15 |
| MSC:
|
65D30 |
| MSC:
|
65H10 |
| MSC:
|
65L06 |
| idZBL:
|
Zbl 0904.65051 |
| idMR:
|
MR1430404 |
| DOI:
|
10.1023/A:1022291010828 |
| . |
| Date available:
|
2009-09-22T17:53:56Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134348 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[5] G. Golub, C.F. Van Loan: Matrix Computations.Baltimore, John Hopkins Univ. Press, 1983. MR 0733103 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[9] L. Jódar, E. Ponsoda: Non-autonomous Riccati type matrix differential equations: existence interval, construction of continuous numerical solutions and error bounds.IMA J. Numer. Anal. 15 (1995), 61–74. MR 1311337, 10.1093/imanum/15.1.61 |
| Reference:
|
[10] J.D. Lambert: Computational Methods in Ordinary Differential Equations.New York, John Wiley, 1962. MR 0423815 |
| Reference:
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[11] P. Lancaster, M. Tismenetsky: The Theory of Matrices. 2nd. ed.New York, Academic Press, 1985. MR 0792300 |
| Reference:
|
[12] P.Chr. Müller: Solution of the matrix equations $AX+XB=-Q$ and $S^TX+XS=-Q$.SIAM J. Appl. Math. 18 (1970), no. 3, 682–687. MR 0260158, 10.1137/0118061 |
| Reference:
|
[13] J.M. Ortega: Numerical Analysis, a Second Course.New York, Academic Press, 1972. Zbl 0248.65001, MR 0403154 |
| Reference:
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[14] W.J. Vetter: Derivative operations on matrices.IEEE Trans. Aut. Control. AC-15 (1970), 241–244. MR 0272801 |
| Reference:
|
[15] S. Wolfram: Mathematica, a System for Doing Mathematics by Computer.Redwood City, Addison Wesley Publishing Co., 1989. |
| . |
