how to update matrix?

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.

[Jan]

Okay. What is your question? What does "u is keeps on increasing with 0.1 in each iteration" mean? Is u a scalar? Do you want to create a loop? What is H? What exactly is the problem? What have you tried so far?

[kitty varghese]

u is a scalar. it is actually my step size.u _italic_should be changed until e=||v-w*h||<0.5.here, v,h,w are matrix.

I want to use this u(which has e<0.5) for my calculation of W= u*W(WH-V)H'

[John BG]

Hi Kitty

this is John BG <mailto:[e-mail] [e-mail]>

Please let me assist you by gathering a few more details about the question:

1.

how big are V and H W?

2.

is V sparse

3.

would you please be so kind that W and H are the upper and lower triangular of V?

4.

is H of V such

h_ij=abs(v_ij) if i=j, h_ij=-abs(v_ij) when i!=j

?

[Jan]

@kitty varghese: Please remember, that the readers in the forum do not have the faintest idea about what you are doing. A statement like "until e=||v-w*h||<0.5" is cryptic, when the meaning of "v, w, h" is unknown and even the norm "||.||" is not uniquely defined in consequence. Is "w" and "W" the same here?

Please edit the original question and insert all details required to understand, what you are doing and what you want to be solved. Posting the current code and explaining the occurring problems is a good idea also.

[John BG]

Jan

there's no need for Kitty to define the norm in the question, because whatever definition, as long as it is a mathematical norm, then it should work in the expression.

It's like, whether using for instance euclidean distance, or city block distance, or any custom norm definition, it doesn't matter, it shouldn't matter.

When applying each different norm it obviously gives different figures but Kitty's expression is general in the sense that

https://www.wolframalpha.com/input/?i=norm

https://en.wikipedia.org/wiki/Norm_(mathematics)

.

[John BG]

Jan, e=||v-w*h||<0.5 means keep decreasing u until e<0.5, provided there is convergence.

In the context of this question, the concise definition of the norm doesn't matter.

Just choose one, the one you like most, whichever you are more familiar with, and use it to calculate the error e.

If the decomposition of the singular (problematic, troublemaker) matrix V is correct, then V is gradually approximated with for instance with the upper triangular and lower triangular matrices.

Probably V cannot be inverted with 1/V (not to be confused here with 1./V) but the processing of V may be possible processing the decomposition of V.

To decompose V, one has to 'precondition' V, but there are different ways to precondition problematic matrices.

Please have a look to Chen's reference in my answer

regards

John BG

<mailto:[e-mail] [e-mail]>

[John BG]

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:[e-mail] [e-mail]>

[Jan]

@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]

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

Answer 1

[John BG]

Hi Kitty

this is John BG <mailto:[e-mail] [e-mail]>

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:[e-mail] [e-mail]>

LIST OF SCRIPTS

help contents

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