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 Post subject: Banded MatrixPosted: Tue, 28 Sep 2010 22:23:20 UTC
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Joined: Mon, 29 Jan 2007 13:48:38 UTC
Posts: 537
Hi there,

On page 12 of the following document:

http://www.finmod.co.za/Hagan_West_curves_AMF.pdf

It shows a banded matrix it also says that the first line sets c = 0 and the last line is

I've looked up what I can on banded matrices and I understand how such matrices can be expressed in a more compact reduced form. But I am still not clear how the matrices shown on page 12 should be multiplied out to give the results stated above?

It can't be straightforward matrix multiplication as the number of columns in matrix A are not equal to the number of rows in x?

Thanks

Baz

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 Post subject: Re: Banded MatrixPosted: Wed, 29 Sep 2010 04:47:20 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Bazman wrote:
Hi there,

On page 12 of the following document:

http://www.finmod.co.za/Hagan_West_curves_AMF.pdf

It shows a banded matrix it also says that the first line sets c = 0 and the last line is

I've looked up what I can on banded matrices and I understand how such matrices can be expressed in a more compact reduced form. But I am still not clear how the matrices shown on page 12 should be multiplied out to give the results stated above?

It can't be straightforward matrix multiplication as the number of columns in matrix A are not equal to the number of rows in x?

Thanks

Baz

It is straightforward matrix multiplication, as long as you remember what actually your more compact form represents. Remember denotes the "wasted" space, and you read each column of the compact form as (sub/./super) diagonal (according to where and how many appears in the column) of a banded matrix. Convert it back to banded matrix and multiply.

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 Post subject: Posted: Wed, 29 Sep 2010 10:39:42 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Mon, 29 Jan 2007 13:48:38 UTC
Posts: 537
So the banded matrix formulation is simply to make displaying and storing the martix easier.

But to carry out any calculations you have to convert it back to its earlier form?

Baz

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 Post subject: Posted: Wed, 29 Sep 2010 12:45:35 UTC
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Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6007
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
Bazman wrote:
So the banded matrix formulation is simply to make displaying and storing the martix easier.

But to carry out any calculations you have to convert it back to its earlier form?

Baz

Well you can avoid converting them back, e.g. using LAPACK's routine DGBSV or similar.

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 Post subject: Posted: Thu, 30 Sep 2010 00:32:05 UTC
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Joined: Mon, 29 Jan 2007 13:48:38 UTC
Posts: 537
thanks OM!!

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