A STABLE NUMERICAL METHOD FOR INVERTING SHAPE FROM MOMENTS

被引：93

作者：

Golub, Gene H. ^{[1
]}

Milanfar, Peyman ^{[2
]}

Varah, James ^{[3
]}

机构：

[1] Stanford Univ, Dept Comp Sci, Stanford, CA 94305 USA

[2] SRI Int, Menlo Pk, CA 94025 USA

[3] Univ British Columbia, Dept Comp Sci, Ctr Integrated Comp Syst Res, Vancouver, BC V6T 1W5, Canada

来源：

SIAM JOURNAL ON SCIENTIFIC COMPUTING | 1999年 / 21卷 / 04期

关键词：

shape; inversion; moments; matrix pencils; polygon; ill-conditioned; quadrature; gravimetry;

D O I：

10.1137/S1064827597328315

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive a stable technique, based upon matrix pencils, for the reconstruction of (or approximation by) polygonal shapes from moments. We point out that this problem can be considered the dual of 2 - D numerical quadrature over polygonal domains. An analysis of the sensitivity of the problem is presented along with some numerical examples illustrating the relevant points. Finally, an application to the problem of gravimetry is explored where the shape of a gravitationally anomalous region is to be recovered from measurements of its exterior gravitational field.

引用

页码：1222 / 1243

页数：22

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