Weird result with Matrix determinant

03172015, 08:16 PM
(This post was last modified: 03172015 08:16 PM by Tugdual.)
Post: #1




Weird result with Matrix determinant
I wanted to calculate the determinant of the matrix
$$\begin{pmatrix} 1 & 0 & 2 & 8 \\ 2 & 1 & 1 & 5 \\ 6 & 3 & 5 & 4 \\ 10 & 4 & 3 & 0 \end{pmatrix}$$ Using Standard number format, Prime Home says 647,000000002 Prime CAS says 647 Home is pretty close but what kind of algorithm can produce such a funny result to calculate a determinant with only integers? Other question is: do we have an explanation for Floating and Rounded Number Formats? Those are recent additions not documented in the user guide. 

03172015, 10:09 PM
Post: #2




RE: Weird result with Matrix determinant
Hi everyone,
When i enter the same matrix on my 28S DET gives me 647,000000002 too ! The 48GX, 49G, 50G give the good answer 647 ! Regards, Damien 

03172015, 11:29 PM
Post: #3




RE: Weird result with Matrix determinant
(03172015 08:16 PM)Tugdual Wrote: Using Standard number format, Well, like any other device with limited working precision (12 resp. 15 digits internally) your calculator will cause a more or less significant roundoff error with every single operation. Evaluating the determinant of a matrix with numerical methods, i.e. not by Cramer's rule or similar exact solutions that are not suitable for larger matrices, usually is done via the wellknown Gauss algorithm resp. a LUdecomposition, leaving the product of the diagonal elements as the desired result. All this involves dozens, if not hundreds of multiplications, divisions and additions. Try a simple example like 2/3 – 2*(1/3) and you'll see how limited the accuracy of even a closetoperfect calculator can be. A tiny error in the least significant digit is a very good result here. With other matrices the error can grow much, much larger. Dieter 

03182015, 08:47 PM
(This post was last modified: 03182015 09:24 PM by Tugdual.)
Post: #4




RE: Weird result with Matrix determinant
Thank you for the explanation Dieter. When using CAS I indeed see fractions on the diagonal of the U matrix so this definitely explains the variation.


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