| A NEW SECANT METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS |
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| 作者姓名： | 盛松柏 邹志鸿 |
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| 作者单位： | Department of Mathematics，Nanjing University，Nanjing 210008，PRC.，Zou Zhi-hong Department of Mathematics，Nanjing University，Nanjing 210008，PRC. |
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| 摘 要： | This paper is concerned with the solution of the nonlinear least squares problems. A new secant method is suggested in this paper, which is based on an affine model of the objective function and updates the first-order approximation each step when the iterations proceed. We present an algorithm which combines the new secant method with Gauss-Newton method for general nonlinear least squares problems. Furthermore, we prove that this algorithm is Q-superlinearly convergent for large residual problems under mild conditions.
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A NEW SECANT METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS |
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| Shcng Song-bai.A NEW SECANT METHOD FOR NONLINEAR LEAST SQUARES PROBLEMS[J].Numerical Mathematics A Journal of Chinese Universities English Series,1993(2). |
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| Authors: | Shcng Song-bai |
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| Institution: | Shcng Song-bai Department of Mathematics,Nanjing University,Nanjing 210008,PRC. Zou Zhi-hong Department of Mathematics,Nanjing University,Nanjing 210008,PRC. |
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| Abstract: | This paper is concerned with the solution of the nonlinear least squares problems. A new secant method is suggested in this paper, which is based on an affine model of the objective function and updates the first-order approximation each step when the iterations proceed. We present an algorithm which combines the new secant method with Gauss-Newton method for general nonlinear least squares problems. Furthermore, we prove that this algorithm is Q-superlinearly convergent for large residual problems under mild conditions. |
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| Keywords: | Secant melhod affine model Gauss-Newton melhod nonlinear least squares |
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