NSolve behaving differently in V9, V10.3 and V10.4

Question

Bug introduced in 10.2 or earlier and fixed in 11.0.0

EDIT In a very fast response from Wolfram they state that this is a known problem and give an example of it working for version 10.4.1.

$Version
(*10.4.1 for Microsoft Windows (64-bit) (April 11, 2016)*)

NSolve[eqn, {h, r, fc}]
(*{{h -> 6944.52 - 3662.26 I, r -> 4.68843*10^10 + 3.07219*10^12 I,   
   fc -> -1.76222*10^8 + 3.51039*10^8 I}, 
  {h -> 0.387583 + 0.0290387 I,  
   r -> 44.9117 - 8.67483 I, fc -> 415.19 + 53.0697 I}} *)

Two solutions are supplied suggesting numerical issues which innaiz has identified below.

The ever helpful Daniel Lichtblau suggests using the "EndomorphismMatrix" method which works well.

sol = NSolve[eqn, {h, r, fc}, Method -> "EndomorphismMatrix"]

(*{{h -> 0.387601 + 0.0289255 I, r -> 44.9137 - 8.66856 I, fc -> 415.189 + 53.0819 I}}*)

One solution is found which satisfies the equations:

eqn /. sol

(* {{True, True, True}} *)

This looks like the way forward.

Original Post

I need to solve equations of the form

eqn = {0.046443987614013964` + 0.3690429826762282` I == 
   h + r/(336.458333332019` - fc), 
  0.8898053473498362` + 0.5457057083738883` I == 
   h + r/(449.9999999982421` - fc), 
  0.6745246773524501` + 0.07315743778713857` I == 
   h + r/(563.5416666644653` - fc)}

So I use NSolve[]

Using Version 9

NSolve[eqn, {h, r, fc}]

(* {{h -> 0.387601 + 0.0289255 I, r -> 44.9137 - 8.66856 I, 
    fc -> 415.189 + 53.0819 I}}*)

Using Version 10.3

(* {{h -> 17838.7 - 12957.1 I, r -> 2.88691*10^12 + 2.45046*10^12 I, 
    fc ->    5.21787*10^7 + 1.8054*10^8 I}, 
   {h -> 0.387583 + 0.0290387 I, r -> 44.9117 - 8.67483 I, 
    fc -> 415.19 + 53.0697 I}} *)

Using Version 10.4

(* {} *)

So the solution is found in Version $9$. In Version $10.3$ there are two solutions, one of which looks like it is a numerical artifact. Finally in Version $10.4$ there is no solution. So is there a bug? I can use Solve but the problem is numeric and NSolve is meant to work better than Solve for numerical cases. What is the solution?

Thanks

You can try one of the methods listed here: (a/103029). It might be considered a backslide, at least on this specific problem, I suppose. See also (a/104429); indeed this might be a duplicate of (104418) — Michael E2, Apr 26 '16 at 11:22
Yes, it is a known issue, reported here and possibly elsewhere. As workaround could do NSolve[eqn, {h, r, fc},Method->"EndomorphismMatrix"]. — Daniel Lichtblau, Apr 26 '16 at 16:18
MMA 11.0.0 seems to have the bug fixed without SetPrecision. It returns {{h -> 0.387601 + 0.0289255 I, r -> 44.9137 - 8.66856 I, fc -> 415.189 + 53.0819 I}} as in MMA 9. — user58955, Aug 14 '16 at 16:29
It worked fine in 10.0.2 and fails in 10.2. So it must have been introduced in 10.1 or 10.2 — Michael E2, Aug 15 '16 at 01:50

score 8 · Answer 1 · edited Apr 27 '16 at 10:45

8

Without SetPrecision it actually doesn't work fine in Mathematica 10.4.1:

In[2]:= NSolve[eqn, {h, r, fc}]

Out[2]= {{h -> 45112.4 + 69798. I, 
  r -> 3.6894*10^11 - 2.09612*10^12 I, 
  fc -> -3.94833*10^7 - 4.35473*10^7 I}, {h -> 0.387583 + 0.0290387 I,
   r -> 44.9117 - 8.67483 I, fc -> 415.19 + 53.0697 I}}

In[3]:= eqn /. %

Out[3]= {{False, False, False}, {False, False, False}}

However, in Mathematica 5.2 it works the same fine way as in version 9 in the subject question:

In[2]:=
NSolve[eqn, {h, r, fc}]

Out[2]=
{{h -> 0.3876007531699076 + 0.028925452482355368*I, 
  r -> 44.913731800940106 - 8.668559624622056*I, 
  fc -> 415.18940593411503 + 53.08192645339874*I}}

In[3]:=
eqn/.%

Out[3]=
{{True,True,True}}

Very sorry, this is not a reason to upgrade.

edited Apr 27 '16 at 10:45

Alexey Popkov

61,809
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answered Apr 26 '16 at 17:25

innaiz

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See How to copy code from Mathematica so it looks good on this site and Hints and help on using the site efficiently and How do I format my posts using Markdown or HTML? and read the FAQ – Apr 26 '16 at 17:34
1

Mathematica 5.2. That's quite a downgrade! Thanks for investigating. – Hugh Apr 26 '16 at 17:41
Usually folks appreciate code that can easily be copied and pasted into Mathematica. Leaving off the In[] and Out[] labels and putting output between comments (*....*) helps with this. I left them in, because it's not that important in this case, imo. You can keep them from showing up be executing SetOptions[$FrontEnd, ExportMultipleCellsOptions -> {"IncludeCellLabels" -> False}]. (+1) – Michael E2 Apr 27 '16 at 10:47

score 4 · Answer 2 · answered Apr 26 '16 at 12:19

4

Works fine in Mathematica 10.4.1

NSolve[SetPrecision[eqn, 16], {h, r, fc}] // Chop
(* {{h -> 0.3876007531699077 + 0.0289254524823553 I, 
  r -> 44.91373180094011 - 8.66855962462205 I, 
  fc -> 415.1894059341150 + 53.0819264533987 I}} *)

answered Apr 26 '16 at 12:19

Thanks for your effort. Perhaps I should upgrade... – Hugh Apr 26 '16 at 16:35

NSolve behaving differently in V9, V10.3 and V10.4

2 Answers2