| 来源类型 | Working Paper
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| 规范类型 | 报告
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| DOI | 10.3386/w0124
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| 来源ID | Working Paper 0124
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| Representing Symmetric Rank Two Updates |
| David M. Gay
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| 发表日期 | 1976-02-01
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| 出版年 | 1976
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| 语种 | 英语
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| 摘要 | Various quasi-Newton methods periodically add a symmetric "correction" matrix of rank at most 2 to a matrix approximating some quantity A of interest (such as the Hessian of an objective function). In this paper we examine several ways to express a symmetric rank 2 matrix [delta] as the sum of rank 1 matrices. We show that it is easy to compute rank 1 matrices [delta1] and [delta2] such that [delta] = [delta1] + [delta2] and [the norm of delta1]+ [the norm of delta2] is minimized, where ||.|| is any inner product norm. Such a representation recommends itself for use in those computer programs that maintain A explicitly, since it should reduce cancellation errors and/or improve efficiency over other representations. In the common case where [delta] is indefinite, a choice of the form [delta1] = [delta2 to the power of T] = [xy to the power of T] appears best. This case occurs for rank 2 quasi- Newton updates [delta] exactly when [delta] may be obtained by symmetrizing some rank 1 update; such popular updates as the DFP, BFGS, PSB, and Davidon's new optimally conditioned update fall into this category. |
| URL | https://www.nber.org/papers/w0124
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| 来源智库 | National Bureau of Economic Research (United States)
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| 引用统计 |
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| 资源类型 | 智库出版物
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| 条目标识符 | http://119.78.100.153/handle/2XGU8XDN/557320
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推荐引用方式
GB/T 7714 |
David M. Gay. Representing Symmetric Rank Two Updates. 1976.
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文件名：
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w0124.pdf
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格式：
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Adobe PDF
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