# Qinian Jin

## Contacts

Contact email:qinian.jin@anu.edu.au

Contact phone:+61 2 6125 3620

Location:Room 4.69, Hanna Neumann Building 145

Associate Professor

### Research interests

- Numerical Analysis
- Inverse Problems
- Partial Differential Equations
- Geometric Analysis

### Groups

- Convenor, Computational mathematics

### Projects

- Supervisor, Inverse problems

- Jin, Q & Wang, W 2018, 'Analysis of the iteratively regularized Gauss-Newton method under a heuristic rule', Inverse Problems, vol. 34, no. 3, pp. 24pp.
- Zhang, Z & Jin, Q 2018, 'Heuristic rule for non-stationary iterated Tikhonov regularization in Banach spaces', Inverse Problems, vol. 34, no. 11, pp. 1-26pp.
- Jiao, Y, Jin, Q, Lu, X et al 2017, 'Preconditioned alternating direction method of multipliers for inverse problems with constraints', Inverse Problems, vol. 33, no. 2, pp. -.
- Jin, Q 2017, 'On a heuristic stopping rule for the regularization of inverse problems by the augmented Lagrangian method', Numerische Mathematik, vol. 136, no. 4, pp. 973-992.
- Jin, Q 2016, 'Landweber-Kaczmarz method in Banach spaces with inexact inner solvers', Inverse Problems, vol. 32, no. 10, pp. 1-26pp.
- Jin, Q & Yang, H 2016, 'Levenbergâ€“Marquardt method in Banach spaces with general convex regularization terms', Numerische Mathematik, vol. 133, no. 4, pp. 655-684.
- Jiao, Y, Jin, Q, Lu, X et al 2016, 'Alternating direction method of multipliers for linear inverse problems', SIAM Journal of Numerical Analysis, vol. 54, no. 4, pp. 2114-2137.
- Jin, Q 2016, 'Hanke-Raus heuristic rule for variational regularization in Banach spaces', Inverse Problems, vol. 32, no. 8, pp. 19pp.
- Hegland, M, Jin, Q & Wang, W 2015, 'Accelerated Landweber iteration with convex penalty for linear inverse problems in Banach spaces', Applicable Analysis, vol. 94, no. 3, pp. 524-547.
- Jin, Q 2015, 'Inexact Newton-Landweber Iteration in Banach Spaces with NonSmooth Convex Penalty Terms', SIAM Journal of Numerical Analysis, vol. 53, no. 5, pp. 2389-2413.
- Jin, Q & Lu, X 2014, 'A fast nonstationary iterative method with convex penalty for inverse problems in Hilbert spaces', Inverse Problems, vol. 30, no. 4, p. 045012.
- Jin, Q & Zhong, M 2014, 'Nonstationary iterated Tikhonov regularization in Banach spaces with uniformly convex penalty terms', Numerische Mathematik, vol. 127, no. 3, pp. 485-513.
- Jin, Q & Wang, W 2013, 'Landweber iteration of Kaczmarz type with general non-smooth convex penalty functionals', Inverse Problems, vol. 29, no. 8, pp. 1-22.
- Jin, Q 2013, 'Further Convergence Results on the General Iteratively Regularized Gauss-Newton Methods Under the Discrepancy Principle', Mathematics of Computation, vol. 82, no. 283, pp. 1647-1665.
- Jin, Q & Mathe, P 2013, 'Oracle Inequality for a Statistical Raus-Gfrerer-Type Rule', SIAM/ASA Journal of Uncertainty Quantification, vol. 1, no. 1, pp. 386-407.
- Jin, Q 2013, 'Solving nonlinear inverse problems by evolution equations based on GaussNewton methods', Applicable Analysis, vol. 92, no. 3, pp. 527-548.
- Jin, Q & Zhong, M 2013, On the iteratively regularized Gauss-Newton method in Banach spaces with applications to parameter identification problems, Numerische Mathematik, vol. 124, no. 4, pp. 647-683.
- Jin, Q 2012, 'On the order optimality of the regularization via inexact Newton iterations', Numerische Mathematik, vol. 121, no. 2, pp. 237-260.
- Jin, Q & Stals, L 2012, 'Nonstationary iterated Tikhonov regularization for ill-posed problems in Banach spaces', Inverse Problems, vol. 28, no. 10.
- Jin, Q 2012, 'Inexact Newton-Landweber iteration for solving nonlinear inverse problems in Banach spaces', Inverse Problems, vol. 28, no. 6, 065002(15pp).
- Jin, Q 2011, 'Newton-type regularization methods for nonlinear inverse problems',
*19th International Congress on Modelling and Simulation, MODSIM 2011*, ed. Felix Chan, Modelling and Simulation Society of Australia and New Zealand Inc., Australia, pp. 385-391. - Jin, Q 2011, 'A General Convergence Analysis of Some Newton-Type Methods for Nonlinear Inverse Problems', SIAM Journal of Numerical Analysis, vol. 49, no. 2, pp. 549-573.
- Jin, Q & Tautenhahn, U 2011, 'Implicit iteration methods in Hilbert scales under general smoothness conditions', Inverse Problems, vol. 27, no. 4, 045012(27pp).
- Jin, Q & Tautenhahn, U 2011, 'Inexact Newton regularization methods in Hilbert scales', Numerische Mathematik, vol. 117, no. 3, pp.555-579.
- Jin, Q 2010, 'On a class of frozen regularized Gauss-Newton methods for nonlinear inverse problems', Mathematics of Computation, vol. 79, no. 272, pp. 2191-2211.
- Jin, Q 2010, 'On a regularized Levenberg-Marquardt method for solving nonlinear inverse problems', Numerische Mathematik, vol. 115, no. 2, pp. 229-259.
- Jin, Q & Tautenhahn, U 2009, 'On the discrepancy principle for some Newton type methods for solving nonlinear inverse problems', Numerische Mathematik, vol. 111, no. 4, pp. 509-558.
- Jin, Q, Li, Y & Xu, H 2008, 'Symmetry and Asymmetry: The Method of Moving Spheres', Advances in Differential Equations, vol. 13, no. 7-8, pp. 601-640.
- Jin, Q 2008, 'A convergence analysis of the iteratively regularized Gaussâ€“Newton method under the Lipschitz condition', Inverse Problems, vol. 24, 045002(16pp).
- Jin, Q, Li, A & Li, Y 2007, 'Estimates and existence results for a fully nonlinear Yamabe problem on manifolds with boundary', Calculus of Variations and Partial Differential Equations, vol. 28, pp. 509-543.
- Jin, Q 2007, 'Local Hessian Estimates for some Conformally Invariant Fully Nonlinear Equations with Boundary Conditions', Differential and Integral Equations, vol. 20, no. 2, pp. 121-132.
- Jin, Q & Li, Y 2006, 'Starshaped compact hypersurfaces with prescribed
*k*-th mean curvature in elliptic space', Discrete and Continuous Dynamical Systems, Series A, vol. 15, no. 2, pp. 367-377. - Jin, Q, Li, Y & Xu, H 2005, 'Nonexistence of Positive Solutions for Some Fully Nonlinear Elliptic Equations', Methods and Applications of Analysis, vol. 12, no. 4, pp. 441-450.
- U Tautenhahn and Q Jin, Tikhonov regularization and a posteriori rules for solving nonlinear ill posed problems, Inverse Problems, 19 (2003), no. 1, 1--21.
- Q Jin and U Amato, A discrete scheme of Landweber iteration for solving nonlinear ill-posed problems, J. Math. Anal. Appl., 253 (2001), no. 1, 187--203.
- U Amato and Q Jin, Convergence of the Red-TOWER method for removing noise from data, IEEE Transaction on Signal Processing, 49(2001), no. 9, 1931--1939.
- Q Jin, A unified treatment of regularization methods for linear ill-posed problems, Numer Math. J Chinese Univ. (English Ser.), 9(2000), no. 1, 111--120.
- Q Jin, Error estimates of some Newton-type methods for solving nonlinear inverse problems in Hilbert scales, Inverse Problems, 16 (2000), no. 1, 187--197.
- Q Jin, On the iteratively regularized Gauss-Newton method for solving nonlinear ill-posed problems, Mathematics of Computation, 69 (2000), no. 232, 1603--1623.
- Q Jin, The analysis of a discrete scheme of the iteratively regularized Gauss-Newton method, Inverse Problems, 16 (2000), no. 5, 1457--1476.
- Q Jin and Z Y Hou, Asymptotic regularization methods for ill-posed linear problems, Chinese Ann. Math. Ser. A, 20(1999), no. 3, 365--374.
- Q Jin and Z Y Hou, On an a posteriori parameter choice strategy for Tikhonov regularization of nonlinear ill-posed problems, Numerische Mathematik, 83 (1999), no. 1, 139--159
- Q Jin, A convergence analysis for Tikhonov regularization of nonlinear ill-posed problems, Inverse Problems, 15 (1999), no. 4, 1087--1098
- Q Jin, Applications of the modified discrepancy principle to Tikhonov regularization of nonlinear ill-posed problems, SIAM J. Numer. Anal. 36 (1999), no. 2, 475--490
- Q Jin, Converse and saturation results on Tikhonov regularization together with a posteriori parameter choice, Sci China Ser A, 42(1999), no. 11, 1137--1146.