| Title:
|
Epsilon-inflation with contractive interval functions (English) |
| Author:
|
Mayer, Günter |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
1998 |
| Pages:
|
241-254 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For contractive interval functions $ [g] $ we show that $ [g]([x]^{k_0}_\epsilon ) \subseteq \int ([x]^{k_0}_\epsilon ) $ results from the iterative process $ [x]^{k+1} := [g]([x]^k_\epsilon ) $ after finitely many iterations if one uses the epsilon-inflated vector $ [x]^k_\epsilon $ as input for $ [g] $ instead of the original output vector $ [x]^k $. Applying Brouwer’s fixed point theorem, zeros of various mathematical problems can be verified in this way. (English) |
| Keyword:
|
epsilon-inflation |
| Keyword:
|
P-contraction |
| Keyword:
|
contraction |
| Keyword:
|
verification algorithms |
| Keyword:
|
interval computation |
| Keyword:
|
nonlinear equations |
| Keyword:
|
eigenvalues |
| Keyword:
|
singular values |
| MSC:
|
65F05 |
| MSC:
|
65F10 |
| MSC:
|
65F15 |
| MSC:
|
65G05 |
| MSC:
|
65G10 |
| MSC:
|
65G50 |
| MSC:
|
65H10 |
| MSC:
|
65H15 |
| MSC:
|
65L05 |
| idZBL:
|
Zbl 0938.65058 |
| idMR:
|
MR1627997 |
| DOI:
|
10.1023/A:1023297204431 |
| . |
| Date available:
|
2009-09-22T17:58:09Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134388 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| . |
