Associate Professor Qinian Jin
Research interests
- Numerical Analysis
- Inverse Problems
- Partial Differential Equations
- Geometric Analysis
Publications
- 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.
Projects and Grants
Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.
- Regularisation methods of inverse problems: theory and computation (Primary Investigator)
- Solving inverse problems with Iterative regularisation and convex penalties (Primary Investigator)
- Regularization methods for solving nonlinear ill-posed inverse problems (Primary Investigator)