Can you comment on when the condition number gives a tight estimate and whether there is a better estimator?

michele

]]>Thanks for the comment and the references. Koev’s paper is available from his web site:

https://math.mit.edu/~plamen/files/acctp.pdf

But maybe I didn’t make this point strongly enough — we can’t use these high accuracy algorithms, for two reasons. First, we only start with a floating point approximation to what would be a totally positive matrix. The roundoff errors made in generating the matrix in the first place have a bigger effect on the inverse than those generated during the inversion process. Second, to take advantage of totally positivity, it is necessary to have the representation as a product of exact, rational, bidiagonal matrices.

— Cleve

]]>-Olga Taussky and Marvin Marcus: Eigenvalues of finite matrices. In John Todd, editor, Survey of Numerical Analysis, pages 279—313. McGraw-Hill, New York, 1962.

The power of this property int the context of computing with high relative accuracy has been shown in

– Plamen Koev: Accurate computations with totally nonnegative matrices. SIAM J. Matrix Anal. Appl. 29(3), pp. 731-751 (2007).

]]>Thanks for the comment. We are certainly aware of the interest in support for quad precision. But, don’t expect it to happen soon.

— Cleve ]]>

Thanks for the interest. My code for @fp128 is not ready for public consumption. It doesn’t yet do correct rounding and doesn’t yet handle quad precision subnormals. I will put it in Cleve’s Laboratory when it is in better shape.

— Cleve ]]>

Thanks for the comment. Yes, we are certainly aware of the interest. But, don’t expect it to happen soon.

— Cleve ]]>

I am sure, that you already know that vpa is very slow and insufficient approach. ]]>

Hope to see this in MATLAB some day!

Can you include your current implementation of @fp128 into Cleve’s Laboratory?

Great post.

Would you consider having 128 Bit support within MATLAB as an official data type?

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