tag:blogger.com,1999:blog-2572826743364240863.post7192009751699547418..comments2016-11-25T14:00:29.857-08:00Comments on The nerdiest of the nerds: Fastest Krylov method for symmetric indefinite problems?HilbertAstronauthttp://www.blogger.com/profile/11443786031975040593noreply@blogger.comBlogger5125tag:blogger.com,1999:blog-2572826743364240863.post-74792876145317137882015-08-31T22:54:34.660-07:002015-08-31T22:54:34.660-07:00The function is the sum of two log-sum-exp functio...The function is the sum of two log-sum-exp functions, which is not strictly convex. Hence, the hessian is not full rank. Also, its condition number, increases based on a parameter. I am seeing that trust region methods like Steihaug or by adding a damping matrix, helps me when the parameter is of low value. For larger values of the parameter, I am hoping a preconditioner will help.Hariprasad Kannanhttps://www.blogger.com/profile/12588742758948945510noreply@blogger.comtag:blogger.com,1999:blog-2572826743364240863.post-31206184655951626742015-08-31T15:21:03.880-07:002015-08-31T15:21:03.880-07:00LSQR should be mathematically equivalent to MINRES...LSQR should be mathematically equivalent to MINRES if the matrix is square and has full rank. CG minimizes the A-norm of the error; MINRES minimizes the 2-norm of the residual.<br /><br />If the matrix does not have full rank, then Newton's method will have problems. If your matrix is ill conditioned but normally has full rank, then you should use a preconditioner. A good preconditioner matters much more for reducing the iteration count than the choice of iterative solver.HilbertAstronauthttps://www.blogger.com/profile/11443786031975040593noreply@blogger.comtag:blogger.com,1999:blog-2572826743364240863.post-50610618267816270232015-08-31T13:10:53.459-07:002015-08-31T13:10:53.459-07:00Thanks a lot for the reply. I am using an iterativ...Thanks a lot for the reply. I am using an iterative solver as part of a truncated Newton method. The truncation rule is classical: a forcing sequence on the residual. Since, MINRES leads to a monotonically decreasing residual, I have seen some people use MINRES. However, people say that LSQR is mathematically equivalent to CG and you have indicated that it has better performance than MINRES. So, I would like to know what is more suitable.Hariprasad Kannanhttps://www.blogger.com/profile/12588742758948945510noreply@blogger.comtag:blogger.com,1999:blog-2572826743364240863.post-10058367975750558972015-08-31T12:28:18.954-07:002015-08-31T12:28:18.954-07:00
If you mean to solve the linear system in a least...<br />If you mean to solve the linear system in a least-squares sense, then use LSQR or LSMR:<br /><br />http://web.stanford.edu/group/SOL/software/lsmr/HilbertAstronauthttps://www.blogger.com/profile/11443786031975040593noreply@blogger.comtag:blogger.com,1999:blog-2572826743364240863.post-2310140374758539792015-08-31T12:23:38.426-07:002015-08-31T12:23:38.426-07:00Hi, What is your suggestion for a positive semidef...Hi, What is your suggestion for a positive semidefinite system (not strictly positive definite), which is highly ill-conditioned and rank deficient?Hariprasad Kannanhttps://www.blogger.com/profile/12588742758948945510noreply@blogger.com