Timeline for Analytic expression for the min value of $g(t):= \sqrt{(t-1)^2 + a^2}+ b|t|$ subject to $|t-1| \le c$
Current License: CC BY-SA 4.0
17 events
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| Jan 10, 2023 at 18:35 | comment | added | Iosif Pinelis | @dohmatob : I have simplified the expression for the minimum using your suggestions. | |
| Jan 10, 2023 at 18:33 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 18:30 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 18:21 | comment | added | dohmatob | Great. Thanks again. BTW, one may observe that the first condition can be compactly written as $0 \le b \le \min(1,\sqrt{c_2/(A + c_2)})$ and second condition can be written as Else.. In the case where $A=0$, this condition reduces to $0 \le b \le 1$, and we get the expression for $m(b,c)$ in the OP. | |
| Jan 10, 2023 at 17:38 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 17:21 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 17:17 | comment | added | Iosif Pinelis | A simple solution without Mathematica is now given. | |
| Jan 10, 2023 at 17:13 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 16:57 | comment | added | dohmatob | OK, thanks, that's helpful. Answer accepted. BTW, do you think that my estimation $M(a,b,c) \asymp a+m(b,c)$ given in the question is sound ? Thanks in advance. | |
| Jan 10, 2023 at 16:45 | comment | added | Iosif Pinelis |
I have explained the meaning of Root.
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| Jan 10, 2023 at 16:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 16:37 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 16:31 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 16:24 | vote | accept | dohmatob | ||
| Jan 10, 2023 at 16:19 | comment | added | dohmatob | Thanks for the detailed answer (upvoted). Algebraic indeed, albeit very thorny. Q: What does Root[f(A,c2,b) #1^2 + #1^4 &, 3] mean ? | |
| Jan 10, 2023 at 16:17 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jan 10, 2023 at 16:07 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |