Re: linear algebra & LAPACK - questions and thoughts

[Rowan Cannaday]

Another deficiency I've noticed in my above solution is that it does not converge for complex eigenvalues.

- Rowan

On Mon, Apr 13, 2020 at 6:07 PM Rowan Cannaday <address@hidden> wrote:

Here is a quick solution to the eigenvalue problem. Should be refined and extended to calculate eigenvectors.

{0~⍨∈⍵×∘.=⍨⍳≢⍵}({r+.×⍉qt⊣(qt r)←⌹[⎕CT]⍵ ;qt;r}⍣{(|⍺)≡|⍵}) 3 3 ⍴ ⍳9
    16.11684397 ¯1.11684397 ¯3.625973215E¯16

As a quick note, my ⎕CT was 1E¯13, however it doesn't seem to zero out the ¯3.625973215E¯16. I suspect this is due to it being a negative number. Its not that big of a hurdle, it can be easily worked around with an extra function. Worlframalpha for example rounds it to 0 in their solution.

Many thanks,

- Rowan

On Mon, Apr 13, 2020 at 5:30 PM Peter Teeson <address@hidden> wrote:

The paper you referred to was a huge epiphany for me. 

Having previously worked in the business world using COBOL and FORTRAN 

the beauty and elegance of APL blew me away. It still does. 

At IPSA we used to model proposed changes (mostly algorithms) to the interpreter in APL first. 

And then wrote the Assembly code to implement.

On Apr 13, 2020, at 11:48 AM, Dr. Jürgen Sauermann <mail@xn--jrgen-sauermann-zvb.de> wrote:

That was my point. If we could establish APL as a language for describing algorithms.  I was thinking
along the lines of Iverson's "Notation as a tool of thought" which is also free now:

https://dl.acm.org/doi/10.1145/358896.358899