how to update matrix?

Question

kitty varghese 2017-8-6

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https://ww2.mathworks.cn/matlabcentral/answers/351722-how-to-update-matrix

编辑： John BG 2017-8-13

i want to update the matrix W .Here W is initialised with radom matrix. Such that W= u*W(WH-V)H'and u is keeps on increasing with 0.1 in each iteration.

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John BG 2017-8-8

Mr Jan Simon

£108 is hard cover brand new, but sure there are cheaper used copies around for sale.

May be there's a copy of this wonderful book written by Chen in the Hildelberg University library.

Matrix preconditioning is a recurring point in any Maths 1st year University course, at least in all engineering modules I have heard of, and many teachers try to reduce the exposure, precisely to avoid questions that may require answer out of scope for a 1st year module.

You can define a particular norm, or you can refer to all norms, any norm, in an abstract way, and then there's no need to define any norm.

So no, Jan, it wouldn't be of any help to define a particular norm, in the context of this question.

If Chen had gone down to define particular norms, and he does in his book, but only here and there, as examples, the publication would require the length of the Encyclopedia Britannica.

And the very useful point is that the MATLAB scripts, you can download the for free, use the links I have supplied.

Chen scripts, actually do have examples with particular norms defined.

Regards

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

Jan 2017-8-8

编辑：Jan 2017-8-8

@John: I do not need explanations about matrix norms, neither from you nor from a book. Therefore this discussion is based on a misunderstanding. As said already, all I wanted to achieve was to encourage kitty to post more details.

John BG 2017-8-8

编辑：John BG 2017-8-13

then, if not for you, for the rest of readers.

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Answer 1

John BG 2017-8-7

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/351722-how-to-update-matrix#answer_277060

在 MATLAB Online 中打开

w_all.zip

Hi Kitty

this is John BG <mailto:jgb2012@sky.com jgb2012@sky.com>

It seems you want to solve a matrix preconditioning problem.

There's a really good book

Matrix Preconditioning Techniques and Applications, by Ke Chen

http://www.cambridge.org/gb/academic/subjects/mathematics/numerical-analysis/matrix-preconditioning-techniques-and-applications?format=HB&isbn=9780521838283

The author freely shares the MATLAB scripts here

https://www.liverpool.ac.uk/maths/ETC/mpta/

in page 174 , the ILU algorithm matches the expression of your question.

I dare say that the solution to your question is already implemented in more than one Chen's scripts, depending on the format of V.

if you find this answer useful would you please be so kind to consider marking my answer as Accepted Answer?

To any other reader, if you find this answer useful please consider clicking on the thumbs-up vote link

thanks in advance

John BG

<mailto:jgb2012@sky.com jgb2012@sky.com>

LIST OF SCRIPTS

help contents

%--- Alphbetical ordering of Mfiles and programs --- Total = 90 files
% ap2f.m
% ap2m.m
% banda.m
% bandb.m
% bandg.m
% bccb.m
% bprod.m
% bttb.m
% cf_split.m
% ch0_w2.m
% ch13.m
% ch3_fmm.m
% ch6_gs.m
% ch6_mg2.m
% ch8.m
% chebg.m
% cheb_fun.m
% circ_pre.m
% circ_toep.m
% cup1.f
% cup2.f
% cup23.in
% cup3.f
% cup4.f
% cup5.f
% cz.m
% def_no.m
% detect.m
% exafft16.m
% fft_fwt.m
% fwt.m
% fwts.m
% ge_all.m
% gh_all.m
% givens.m
% gj_ek.m
% gmrest_k.m
% gmres_c.m
% gmres_k.m
% gmres_nr.m
% g_e.m
% g_h.m
% g_j.m
% hb1.m
% hess_as.m
% hopf.m
% houses.m
% ifwt.m
% ilu_0.m
% ilu_t.m
% index2.m
% intera.m
% iperm0.m
% iperm2.m
% iter3.m
% iwts.m
% lap_lab.m
% matrix0.mat
% matrix1.mat
% matrix2.mat
% matrix3.mat
% mat_pr0.m
% mat_prt.m
% mat_prt4.m
% mgm_2d.m
% mgm_2f.m
% mgm_2s.m
% mgs.m
% mk_ek.m
% multic.m
% mygrid.m
% my_jordan.m
% nsh.m
% perm0.m
% perm2.m
% richa_nr.m
% run8.m
% run9.m
% run_ai.m
% schts.m
% size6.rua
% size6.m
% spai2.m
% spyc.m
% t_band.m
% t_dete.m
% wathen.m
% waz.m
% waz_all.m
% waz_t.m

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