Dgdrxrt

Can smartphones with the same camera sensor have different image quality?

Didn't get enough time to take a Coding Test - what to do now?

Can a novice safely splice in wire to lengthen 5V charging cable?

Hiding Certain Lines on Table

Can the DM override racial traits?

Match Roman Numerals

ELI5: Why do they say that Israel would have been the fourth country to land a spacecraft on the Moon and why do they call it low cost?

How can I protect witches in combat who wear limited clothing?

The variadic template constructor of my class cannot modify my class members, why is that so?

Do working physicists consider Newtonian mechanics to be "falsified"?

Road tyres vs "Street" tyres for charity ride on MTB Tandem

Is it ok to offer lower paid work as a trial period before negotiating for a full-time job?

Did the UK government pay "millions and millions of dollars" to try to snag Julian Assange?

Was credit for the black hole image misattributed?

Mortgage adviser recommends a longer term than necessary combined with overpayments

What can I do if neighbor is blocking my solar panels intentionally?

What is special about square numbers here?

Do warforged have souls?

Does Parliament hold absolute power in the UK?

Why can't wing-mounted spoilers be used to steepen approaches?

Why can't devices on different VLANs, but on the same subnet, communicate?

How should I replace vector<uint8_t>::const_iterator in an API?

Windows 10: How to Lock (not sleep) laptop on lid close?

Python - Fishing Simulator

Find the value of $n$ that minimizes a complicated integral

0

$begingroup$

I need to approximate this function:

$$f(x)=left{beginmatrix
sqrt21.49-(x+1.28)^2 textif x<-3.17\
sqrt60.56-x^2 -2.87 textif -3.17leq xleq 3.17\
sqrt21.49-(x-1.28)^2 textif x>3.17
endmatrixright.$$

With a more simple one. I found out that:

$$g(x)=4.91left(1-frac4x^211.84^2right)^frac1n$$

Works really well for some value of $n$ . To optimize the value of this parameter I'm trying to minimize the middle error integral:

$$E=fracf(x)-g(x)11.84$$

With some little tricks(for example noticing that the two functions are even, and noticing that an ellipse approximates pretty well $f$ so $napprox 2$) and using Geogebra I managed to find:

$$n_optimalapprox 2.2 $$

But I can't go deeper with the precision because Geogebra is a limitated software. Can you help me with a more powerful software in finding a more precise value for $n_optimal$

[Important!: the extremes of integration are a bit approximated, the precise value should be $pm 5.915...$]

Thank you :)

optimization approximation

share|cite|improve this question

asked Mar 31 at 14:20

EurekaEureka

862114

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Check out Desmos calculator: desmos.com/calculator/7url7y2c7d.
  $endgroup$
  – kccu
  Mar 31 at 14:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @kccu thank you :)
  $endgroup$
  – Eureka
  Mar 31 at 18:00
  

  
  
  
  

add a comment | 

0

$begingroup$

I need to approximate this function:

$$f(x)=left{beginmatrix
sqrt21.49-(x+1.28)^2 textif x<-3.17\
sqrt60.56-x^2 -2.87 textif -3.17leq xleq 3.17\
sqrt21.49-(x-1.28)^2 textif x>3.17
endmatrixright.$$

With a more simple one. I found out that:

$$g(x)=4.91left(1-frac4x^211.84^2right)^frac1n$$

Works really well for some value of $n$ . To optimize the value of this parameter I'm trying to minimize the middle error integral:

$$E=fracf(x)-g(x)11.84$$

With some little tricks(for example noticing that the two functions are even, and noticing that an ellipse approximates pretty well $f$ so $napprox 2$) and using Geogebra I managed to find:

$$n_optimalapprox 2.2 $$

But I can't go deeper with the precision because Geogebra is a limitated software. Can you help me with a more powerful software in finding a more precise value for $n_optimal$

[Important!: the extremes of integration are a bit approximated, the precise value should be $pm 5.915...$]

Thank you :)

optimization approximation

share|cite|improve this question

asked Mar 31 at 14:20

EurekaEureka

862114

$endgroup$

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  Check out Desmos calculator: desmos.com/calculator/7url7y2c7d.
  $endgroup$
  – kccu
  Mar 31 at 14:36
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @kccu thank you :)
  $endgroup$
  – Eureka
  Mar 31 at 18:00
  

  
  
  
  

add a comment | 

$begingroup$

I need to approximate this function:

$$f(x)=left{beginmatrix
sqrt21.49-(x+1.28)^2 textif x<-3.17\
sqrt60.56-x^2 -2.87 textif -3.17leq xleq 3.17\
sqrt21.49-(x-1.28)^2 textif x>3.17
endmatrixright.$$

With a more simple one. I found out that:

$$g(x)=4.91left(1-frac4x^211.84^2right)^frac1n$$

Works really well for some value of $n$ . To optimize the value of this parameter I'm trying to minimize the middle error integral:

$$E=fracf(x)-g(x)11.84$$

With some little tricks(for example noticing that the two functions are even, and noticing that an ellipse approximates pretty well $f$ so $napprox 2$) and using Geogebra I managed to find:

$$n_optimalapprox 2.2 $$

But I can't go deeper with the precision because Geogebra is a limitated software. Can you help me with a more powerful software in finding a more precise value for $n_optimal$

[Important!: the extremes of integration are a bit approximated, the precise value should be $pm 5.915...$]

Thank you :)

optimization approximation

share|cite|improve this question

asked Mar 31 at 14:20

EurekaEureka

862114

$endgroup$

share|cite|improve this question

asked Mar 31 at 14:20

EurekaEureka

862114

share|cite|improve this question

asked Mar 31 at 14:20

EurekaEureka

862114

asked Mar 31 at 14:20

EurekaEureka

862114

asked Mar 31 at 14:20

EurekaEureka

862114