Numerical Algorithms ( IF 2.1 ) Pub Date : 2020-03-24 , DOI: 10.1007/s11075-019-00835-2 Xiongfeng Song , Wei Xu , Ken Hayami , Ning Zheng
The variable projection method is a classical and efficient method for solving separable nonlinear least squares (SNLLS) problems. However, it is hard to handle the constrained SNLLS problems since the explicit form of the Jacobian matrix is required in each iteration. In this paper, we propose a secant variable projection (SVP) method, which employs a rank-one update to estimate the Jacobian matrices. The main advantages of our method are efficiency and ease of applicability to constrained SNLLS problems. The local convergence of our SVP method is also analyzed. Finally, some data fitting and image processing problems are solved to compare the performance of our proposed method with the classical variable projection method. Numerical results illustrate the efficiency and stability of our proposed SVP method in solving the SNLLS problems arising from the blind deconvolution problems.
中文翻译:
求解非负可分离最小二乘问题的割线变投影方法
可变投影法是解决可分离的非线性最小二乘(SNLLS)问题的经典有效方法。但是,由于每次迭代都需要Jacobian矩阵的显式形式,因此很难处理受约束的SNLLS问题。在本文中,我们提出了割线变量投影(SVP)方法,该方法采用秩一更新来估计Jacobian矩阵。我们方法的主要优点是效率高,并且易于解决受约束的SNLLS问题。还分析了我们的SVP方法的局部收敛性。最后,解决了一些数据拟合和图像处理问题,以将我们提出的方法与经典可变投影方法的性能进行比较。