A multi-level algorithm for the solution of moment problems
A multi-level algorithm for the solution of moment problems
复制标题
求解矩问题的多级算法
DOI：
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发表时间：
1999
期刊：
影响因子：
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通讯作者：
T. Strohmer
中科院分区：
文献类型：
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作者：
O. Scherzer;T. Strohmer
本文研究了一般线性矩量问题的数值解法，其中的解属于Hilbert空间的一个嵌套子空间族。提出了基于共轭梯度法和Landweber-Richardson方法的多级算法，该算法从数值计算过程中出现的量确定“最佳”重建水平。作为一个重要的例子，我们讨论了重建带限信号从不规则间隔的噪声样本，当信号的实际带宽是不可用的。数值算例表明了算法的有效性
We study numerical methods for the solution of general linear moment problems, where the solution belongs to a family of nested subspaces of a Hilbert space. Multi-level algorithms, based on the conjugate gradient method and the Landweber-Richardson method are proposed that determine the "optimal" reconstruction level a posteriori from quantities that arise during the numerical calculations. As an important example we discuss the reconstruction of band-limited signals from irregularly spaced noisy samples, when the actual bandwidth of the signal is not available. Numerical examples show the usefulness of the proposed algorithms