LFD Book Forum Chapter 4 Problem 4.4

#1
09-17-2013, 08:39 PM
 GB449 Member Join Date: Aug 2013 Posts: 20
Chapter 4 Problem 4.4

I have the following questions. I have a few more on using Legendre polynomials but I will read 4.3 first before asking

a) what does selecting independently with P(x) mean? In earlier homework, we selected the points at random from [-1,1] which was clear to me - I used a random function with min = -1 and max = +1 but I am not clear what to do with P(x)

b) is clear since it is f(). Should we generate random numbers for each ? If so, what are the min and max values for the random numbers?

Thank you!
#2
09-19-2013, 05:09 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 4 Problem 4.4

Quote:
 Originally Posted by GB449 a) what does selecting independently with P(x) mean? In earlier homework, we selected the points at random from [-1,1] which was clear to me - I used a random function with min = -1 and max = +1 but I am not clear what to do with P(x)
In this problem P(x) is the uniform probability distribution on [-1,+1] and so what you did in the earlier homework is exactly what this means -- generate a random number between -1 and +1. In general, the way to generate may not be uniformly random over [-1,+1]. It is that specifies the input probability distribution. For example, if is the Gaussian distribution with mean 0 and variance 1, then you would generate each from that Gaussian distribution.

Quote:
 b) is clear since it is f(). Should we generate random numbers for each ? If so, what are the min and max values for the random numbers?
Note . Each should be an independent Gaussian random number with mean 0 and variance 1 (you then multiply this random number by ).
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#3
09-21-2013, 01:24 AM
 GB449 Member Join Date: Aug 2013 Posts: 20
Re: Chapter 4 Problem 4.4

Thank you for the reply! How can I generate Gaussian random numbers with mean 0 and variance 1? I am programming in C#.
#4
09-21-2013, 05:33 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 4 Problem 4.4

Quote:
 Originally Posted by GB449 Thank you for the reply! How can I generate Gaussian random numbers with mean 0 and variance 1? I am programming in C#.
This is a common task for which standard algorithms exist in most numerical packages. For example, in matlab there is a function . You can also do this using the Box-Muller transform. You may find this thread useful:

http://stackoverflow.com/questions/2...sian-variables
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#5
12-03-2014, 01:06 PM
 Kleber de Aguiar Junior Member Join Date: Dec 2014 Posts: 1
Re: Chapter 4 Problem 4.4

Hello,

What I supposed to do to select the coefficients ai, in order to respect the restriction of Ea,x [f^2] = 1 ?

Best regards,
Kleber
#6
01-12-2015, 11:15 PM
 ypeels Member Join Date: Dec 2014 Posts: 17
Re: Chapter 4 Problem 4.4

Quick question: what does the "LAMi" at the beginning of the problem mean?
#7
01-13-2015, 07:05 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 4 Problem 4.4

Spurious typo that snuck in, sorry.
Quote:
 Originally Posted by ypeels Quick question: what does the "LAMi" at the beginning of the problem mean?
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#8
01-13-2015, 07:06 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Chapter 4 Problem 4.4

Rescale all the weights by a constant factor so that Ea,x [f^2] = 1.
Quote:
 Originally Posted by Kleber de Aguiar Hello, just another question about this problem: What I supposed to do to select the coefficients ai, in order to respect the restriction of Ea,x [f^2] = 1 ? Best regards, Kleber
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#9
07-05-2018, 11:52 PM
 715073608 Member Join Date: May 2018 Posts: 12
Re: Chapter 4 Problem 4.4

Dear professor,can you explain what does the question(e) mean and how can I draw the pictures on page 144?Thank you .

 Tags chapter 4, lecture 11

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