| 来源类型 | Working Paper
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| 规范类型 | 报告
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| DOI | 10.3386/w0125
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| 来源ID | Working Paper 0125
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| On Modifying Singular Values to Solve Possible Singular Systems of Non-Linear Equations |
| David M. Gay
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| 发表日期 | 1976-03-01
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| 出版年 | 1976
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| 语种 | 英语
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| 摘要 | We show that if a certain nondegeneracy assumption holds, it is possible to guarantee the existence of a solution to a system of nonlinear equations f(x) = 0 whose Jacobian matrix J(x) exists but maybe singular. The main idea is to modify small singular values of J(x) in such away that the modified Jacobian matrix J^(x) has a continuous pseudoinverse J^+(x)and that a solution x* of f(x) = 0 may be found by determining an asymptote of the solution to the initial value problem x(0) = x[sub0}, x’(t) = -J^+(x)f(x). We briefly discuss practical (algorithmic) implications of this result. Although the nondegeneracy assumption may fail for many systems of interest (indeed, if the assumption holds and J(x*) is non-singular, then x is unique), algorithms using(x) may enjoy a larger region of convergence than those that require(an approximation to) J[to the -1 power[(x). |
| URL | https://www.nber.org/papers/w0125
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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/557321
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推荐引用方式
GB/T 7714 |
David M. Gay. On Modifying Singular Values to Solve Possible Singular Systems of Non-Linear Equations. 1976.
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文件名：
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w0125.pdf
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格式：
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Adobe PDF
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