Fredag 4 december 2015, Oleg Burdakov, MAI, Linköpings universitet
Talare: Oleg Burdakov, MAI, Linköpings universitet
Titel: On Jacobian matrix approximations and their application in solving nonlinear equation and least-squares problems
Tid och plats: Fredag 4 december 2015, Hopningspunkten, 13:15-14:15
Sammanfattning: Our involvement in solving inverse problems in diffuse reflectance spectroscopy and laser Doppler flowmetry stimulated our activity in developing efficient Jacobiam matrix approximations of various types. These inverse problem are constrained nonlinear least squares problems involving a regularization. For solving them, we applied a Broyden-type quasi-Newton approximation of the first derivatives (the Jacobian matrix) of the model with respect to its parameters. Bearing in mind that, for the medical equipment mentioned above, the solution time is a critical parameter, we focused on more efficient Jacobian approximations adopted to solving the related inverse problem. We developed efficient multipoint secant and also interpolation-type approximations of the Jacobian matrix. The numerical experiments show that the new approximations are more accurate than those produced by Broyden's updating formula. This requires less number of iterations for solving the mentioned problem, and as the result, less number of calls of the model which constitutes the major part of the computational time. The aim of this talk is to present our results related to Jacobiam matrix approximations.
Senast uppdaterad: 2015-11-30