| WANG XINGHUA.[J].数学年刊A辑,1980,1(2):283~288 |
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| ON THE MYSOVSKICH THEOREM OF NEWTONS METHOD |
| Received:October 03, 1979 |
| DOI： |
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| 英文摘要: |
| In a real or oompbx Banach space X, let P be an operator with Lipsohitz
continnous Frechet derivative P', and \[{X_*} \in X\] such that \[P({X_*}) = 0\] and \[{P^'}{({X_*})^{ - 1}}\] exists.
It is shown that a ball with center \[{X_*}\] and best possible radius such that the theorem of
Mysoyskich guarantees convergenee of Newton's method to \[{X_*}\] starting from any point
\[{x_0}\] in ihe ball (theorem 3). In comparison with the corresponding results of Rall's work
on Kantorovich theorem, the radius obtained is smaller than that from Kantorovich
theorem. Therefore we suggest here an improved form of Mysoyskich theorem (theorem
1) . Thus, the corresponding value of the radius is augmented beyond that from
Kantorovich theorem (theorem 2). |
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