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0

$begingroup$

$(f,g)= int_0^1 x^2 f(x) g(x) dx$

I need to find corresponding orthagonal function $phi_0,phi_1$ where $phi_0 = 1$

and $w(x) = x^2$ (weight function)

$phi_1(x) = (x - alpha_0)phi_0 $

Where $alpha_0 = frac(phi_0,xphi)^2$

so I did $alpha_0 = frac(phi,xphi)^2 = fracint_0^1 x^2.xdxint_0^1 1.1dx = frac1/41 = 1/4$
so

$phi_1 =x - 1/4$

is this the right place and time to put weight fucntion $x^2$ in side the integral multiplying $xdx$

problem is when I check this function $int_0^1 w(x)phi_1 phi_2 $ its not equal to zero. ie $int_0^1 x^2.1.(x - frac14)dx ne 0 $

calculus algebra-precalculus

share|cite|improve this question

edited Mar 11 at 21:29

tt z

asked Mar 11 at 3:53

tt ztt z

265

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It's not entirely clear what's going on here. Are you trying to produce a basis of some vector space of polynomials orthonormal with respect to the given inner product $(f, g) := int_0^1 x^2 f(x) g(x) dx$?
  $endgroup$
  – Travis
  Mar 11 at 20:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes trying to find corresponding orthonormal functions.
  $endgroup$
  – tt z
  Mar 11 at 21:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Perhaps post a statement of the original question, for clarity?
  $endgroup$
  – Travis
  Mar 11 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $(f,g)= int_0^1 x^2 f(x) g(x) dx$ is inner production function. Determined the corresponding orthogonal function $ phi_0 phi_1. phi_2$<question ends> I know from other exercise that we start with $phi_0 = 1$
  $endgroup$
  – tt z
  Mar 11 at 21:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I meant, edit your original post to include it. But either way---what are the constraints on $phi_1, phi_2$? There's no way to answer this question without more context.
  $endgroup$
  – Travis
  Mar 11 at 21:17
  
  

  
  
  
  

add a comment | 

0

$begingroup$

$(f,g)= int_0^1 x^2 f(x) g(x) dx$

I need to find corresponding orthagonal function $phi_0,phi_1$ where $phi_0 = 1$

and $w(x) = x^2$ (weight function)

$phi_1(x) = (x - alpha_0)phi_0 $

Where $alpha_0 = frac(phi_0,xphi)^2$

so I did $alpha_0 = frac(phi,xphi)^2 = fracint_0^1 x^2.xdxint_0^1 1.1dx = frac1/41 = 1/4$
so

$phi_1 =x - 1/4$

is this the right place and time to put weight fucntion $x^2$ in side the integral multiplying $xdx$

problem is when I check this function $int_0^1 w(x)phi_1 phi_2 $ its not equal to zero. ie $int_0^1 x^2.1.(x - frac14)dx ne 0 $

calculus algebra-precalculus

share|cite|improve this question

edited Mar 11 at 21:29

tt z

asked Mar 11 at 3:53

tt ztt z

265

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  It's not entirely clear what's going on here. Are you trying to produce a basis of some vector space of polynomials orthonormal with respect to the given inner product $(f, g) := int_0^1 x^2 f(x) g(x) dx$?
  $endgroup$
  – Travis
  Mar 11 at 20:53
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Yes trying to find corresponding orthonormal functions.
  $endgroup$
  – tt z
  Mar 11 at 21:08
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Perhaps post a statement of the original question, for clarity?
  $endgroup$
  – Travis
  Mar 11 at 21:09
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $(f,g)= int_0^1 x^2 f(x) g(x) dx$ is inner production function. Determined the corresponding orthogonal function $ phi_0 phi_1. phi_2$<question ends> I know from other exercise that we start with $phi_0 = 1$
  $endgroup$
  – tt z
  Mar 11 at 21:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I meant, edit your original post to include it. But either way---what are the constraints on $phi_1, phi_2$? There's no way to answer this question without more context.
  $endgroup$
  – Travis
  Mar 11 at 21:17
  
  

  
  
  
  

add a comment | 

$begingroup$

$(f,g)= int_0^1 x^2 f(x) g(x) dx$

I need to find corresponding orthagonal function $phi_0,phi_1$ where $phi_0 = 1$

and $w(x) = x^2$ (weight function)

$phi_1(x) = (x - alpha_0)phi_0 $

Where $alpha_0 = frac(phi_0,xphi)^2$

so I did $alpha_0 = frac(phi,xphi)^2 = fracint_0^1 x^2.xdxint_0^1 1.1dx = frac1/41 = 1/4$
so

$phi_1 =x - 1/4$

is this the right place and time to put weight fucntion $x^2$ in side the integral multiplying $xdx$

problem is when I check this function $int_0^1 w(x)phi_1 phi_2 $ its not equal to zero. ie $int_0^1 x^2.1.(x - frac14)dx ne 0 $

calculus algebra-precalculus

share|cite|improve this question

edited Mar 11 at 21:29

tt z

asked Mar 11 at 3:53

tt ztt z

265

$endgroup$

share|cite|improve this question

edited Mar 11 at 21:29

tt z

asked Mar 11 at 3:53

tt ztt z

265

share|cite|improve this question

edited Mar 11 at 21:29

tt z

asked Mar 11 at 3:53

tt ztt z

265

asked Mar 11 at 3:53

tt ztt z

265

asked Mar 11 at 3:53

tt ztt z

265