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I've seen this on several threads in MATLAB central, but haven't found a suitable solution. Here are some properties of A: 
Sometimes the following iterative algorithm works well: 
Could you provide some information about this method (name, paper, ...)? Also, if A is size m x n, then sum(A,2) will be of size, m x 1 so, I don't understand that step. 
Subject: min Axb for large sparse A From: Bruno Luong Date: 22 Jun, 2010 19:28:21 Message: 4 of 21 
"Jacob " <mithunjacob_oohay@yahoo.com> wrote in message <hvqrvj$irq$1@fred.mathworks.com>... 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvr2sl$odb$1@fred.mathworks.com>... 
Subject: min Axb for large sparse A From: Bruno Luong Date: 22 Jun, 2010 21:15:25 Message: 6 of 21 
Sorry Matt, in optimization the poor performance of gradient method is one of the first lesson students leaned in school. This is no surprise for anyone. Try this example: after 10 iterations your algorithm is still far from being not converge, whereas a simple conjugate gradient converge in 2 iterations. 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvr95c$lhj$1@fred.mathworks.com>... 
Subject: min Axb for large sparse A From: Bruno Luong Date: 23 Jun, 2010 03:04:05 Message: 8 of 21 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hvrffq$fvc$1@fred.mathworks.com>... 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvrtj5$e7m$1@fred.mathworks.com>... 
Subject: min Axb for large sparse A From: Bruno Luong Date: 23 Jun, 2010 13:15:20 Message: 10 of 21 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hvsud5$hdt$1@fred.mathworks.com>... 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvt1d8$3dc$1@fred.mathworks.com>... 
Your discussion regarding the matter seems great, and I must admit your simple method works very well for my matrix (which is highly diagonalized). 
"Jacob " <mithunjacob_oohay@yahoo.com> wrote in message <hvt7ds$ctr$1@fred.mathworks.com>... 
Subject: min Axb for large sparse A From: Bruno Luong Date: 23 Jun, 2010 16:24:04 Message: 14 of 21 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hvt6p8$hj$1@fred.mathworks.com>... 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hvtaj4$c1n$1@fred.mathworks.com>... 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvtcf4$epi$1@fred.mathworks.com>... 
Subject: min Axb for large sparse A From: Bruno Luong Date: 24 Jun, 2010 06:33:25 Message: 17 of 21 
"Matt J " <mattjacREMOVE@THISieee.spam> wrote in message <hvuipd$qre$1@fred.mathworks.com>... 
"Bruno Luong" <b.luong@fogale.findmycountry> wrote in message <hvuu7l$2ms$1@fred.mathworks.com>... 
Thanks for the proof, but do you have any citable material? Papers/textbooks/etc? 
"Jacob " <foobar@yahoo.com> wrote in message <i0i09k$99m$1@fred.mathworks.com>... 
Dear Jacob, Matt and Bruno, 
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