残余物
适定问题
正规化(语言学)
计算机科学
数学优化
规范(哲学)
算法
数学
噪声数据
应用数学
人工智能
政治学
法学
作者
Per Christian Hansen,Misha E. Kilmer,Rikke Høj Kjeldsen
出处
期刊:Bit Numerical Mathematics
日期:2006-03-01
卷期号:46 (1): 41-59
被引量:125
标识
DOI:10.1007/s10543-006-0042-7
摘要
Most algorithms for choosing the regularization parameter in a discrete ill-posed problem are based on the norm of the residual vector. In this work we propose a different approach, where we seek to use all the information available in the residual vector. We present important relations between the residual components and the amount of information that is available in the noisy data, and we show how to use statistical tools and fast Fourier transforms to extract this information efficiently. This approach leads to a computationally inexpensive parameter-choice rule based on the normalized cumulative periodogram, which is particularly suited for large-scale problems.
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