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lvl10720-Turquoise
20-Turquoise
October 14, 2018
Solved

"No solution was found". What does it mean in this case ?

  • October 14, 2018
  • 3 replies
  • 4413 views

  Hello, Everyone.

  From :

( I ).PNG

      "No solution was found". What does it mean in this case ?

             Regards.

3 replies

V
24-Ruby IV
ValeryOchkov24-Ruby IV
24-Ruby IV
October 14, 2018

One plot solution

g_x.png

W
Werner_E25-Diamond I
25-Diamond I
October 14, 2018

Valery, your plot is missing two of the four solution intervals.

W
Werner_E25-Diamond IAnswer
25-Diamond I
October 14, 2018

See here: https://community.ptc.com/t5/PTC-Mathcad/Finding-local-min/m-p/576186/highlight/true#M182810

L
lvl10720-TurquoiseAuthor
20-Turquoise
October 16, 2018

and how many solutions the f(x) have ?

( A ).PNG

W
Werner_E25-Diamond I
25-Diamond I
October 17, 2018
@lvl107 wrote:

and how many solutions the f(x) have ?

 

Five!

But the length of the five solution intervals are very small (in the range of 10^-8) so you may run into numerical problems when you try to plot.

Because five is an odd number, now B1 in the picture below consists of all the lower limits of the solution intervals and B2 holds all the upper limits.

 

The intervals you are interested in are the tiny areas between the points where the red curve crosses the dotted blue line (slightly above zero) up to the point where it crosses the green line (slightly below zero).

The picture shows a zoomed view for the first and the last solution interval.

B.png

W
Werner_E25-Diamond I
25-Diamond I
October 17, 2018

One additional remark:

The absolute value usually is quite beastly - either when it comes to solving equations and inequalities and also when it comes to derivatives. So its always a good idea to avoid the absolute value and either replace the calculations by separate calculations (like I did it above to get the limits of the intervals) or use squaring instead of the absolute value (see below).
BTW thats also one reason why in regression analysis we use the squares of the errors instead of their absolute value - the latter would be far more difficult to handle.

B2.png

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