Solving a quadratic matrix equation by newton's method with exact line searches (Q2784348)
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scientific article; zbMATH DE number 1732243
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solving a quadratic matrix equation by newton's method with exact line searches |
scientific article; zbMATH DE number 1732243 |
Statements
23 April 2002
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quadratic matrix equation
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solvent
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Newton's method
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generalized Sylvester equation
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exact line searches
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quadratic eigenvalue problem
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condition number
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backward error analysis
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numerical examples
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global convergence
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0.96591234
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0.94398534
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0.9333076
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0.9158057
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0.9031133
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0.9010059
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0.89905876
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Solving a quadratic matrix equation by newton's method with exact line searches (English)
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The authors show how to incorporate line searches into Newton's method for solving the quadratic matrix equation \(AX^2+ BX+ C= 0\), where \(A\), \(B\) and \(C\) are square matrices. The paper merits from two main contributions: (1) incorporation of line searches to improve global convergence and (2) derivation of a true condition number for the matrix equation and backward error analysis of the approximate solution. Numerical examples calculated via MATLAB illustrate the feasibility of the approach.
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