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These are questions asked by student_md

where

and .

Also,

 

MY TRY: You can download the code.mw

restart:
with(LinearAlgebra):
interface(rtablesize=20):
with(plots):
k:=2:M:=2:
Tm:=(t,m)-> 2*t*Tm(t,m-1)-Tm(t,m-2);
Tm(t,0):=1:
Tm(t,1):=t:

Tm2:=(tt,m)->subs(t=tt,Tm(t,m)): 
alpha:=(m)->piecewise(m=0,1/sqrt(Pi),sqrt(2)/sqrt(Pi));
psii:=(n,m,x)->piecewise((n-1)/(2^(k-1)) <= x and x <= n/(2^(k-1)),
alpha(m)*(2^(k/2))*Tm2(2^k*x-2*n+1,m), 0); 
psi:=(t)->Array([seq(seq(psii(i,j,t),j=0..M-1),i=1...2^(k-1))] ):
for i from 1 to ((2^(k-1))*M) do
r[i]:=evalf(psi((2*i-1)/((2^k)*M))):
end do:
m:=M*(2^(k-1)):
xi:=(i,n)->((i+1)^(n+1)-2*i^(n+1)+(i-1)^(n+1));
PB_n:=Matrix(m,m)

 

Could you help me to complete the code?

Best regards.

I want to find following NxN matrix P                                           (N=2^k.M where k and M are a positive integers)  

My Code Try: question.mw

restart:
with(LinearAlgebra):
interface(rtablesize=20):
k:=2:
M:=4:
N:=2^k*M: 
for i from 1 to M do
S:= (sqrt(2)/2^k)*Matrix(M,M, (i,j)-> `if`(`and`(i::odd,j=1) ,-1/(i*(i-2)),0)):   
end do:
C:= (1/2^k)*BandMatrix( [ [ seq(-1/(2*sqrt(2)*(i-1)*(i-3)), i=4..M)], [ 1, seq(0*i,i=1..M-1) ],[ seq(4/2*(i-3),i=2..M)]
                ]
              ); #I think the matrix C is not same in the question
     
Gen:=proc(K::posint,A,B)
  Matrix(scan=triangular[upper],[seq([A,seq(B,i=j..2^(K)-1)],j=1..2^(K))]);
end proc: 
P:=Gen(k,C,S);

question.mw

Hi,

I have a numeric method for solving differential equations. You can find the Maple code.

 numeric_method.mw

 Question: In the method, we have 10^(-6) decimal error. How to quickly find the which decimal error by Maple? What are your suggestions? 

-Can we solve symbolically matrix equations where the matrices are ungiven by MAPLE?

For a simple example;

Let A.B+2B=C.

where A nxn is matrix and B, C and nx1 matrices. (all matrices are ungiven)

Question: Find symbolically matrix B in terms of C and A?

My try:

We can quickly calculate Matrix B by hand.  We have (A+2I)B=C and so B=(A+2I)^(-1).C   ( where (A+2I) is invertible and I is nxn identity matrix)

Briefly: Can we do for the more complex and difficult equations by MAPLE? 

My question has two steps:

STEP 1:  The multiplication  of is defined as follows

 

if n<>l, then

.

if n=l and m<=s,

Question 1: I wrote a code for calculating the multiplication  of. Is it right?

The code for Step 1  

restart;

multiply:=proc(n,m,l,s) local g,a: 
a:=unapply(doublefactorial(2*j-1)/factorial(j),j):
g:=unapply((a(m-j)*a(j)*a(s-j)/a(m+s-j))*(2*m+2*s-4*j+1)/(2*m+2*s-2*j+1),j):

if n<>l then 0 else
sqrt((2*m+1)*(2*s+1))*2^(K/2-1).add((g(j)/sqrt(m+s-2*j+1/2))*phi[n, m+s-2*j],j=0..m) 
end if
end proc:
 
n:=2:
l:=2:
m:=1:
s:=1:
multiply(n,m,l,s);

when I compared the results which I got and the results which is given in the book as follows, I think it is right.

Step 2:

We know that the outer product matrix is calculated as follows 

  

We found the elements of the outer product matrix in Step 1. 

Question 2 : I want to write the elements which are derived in step 1 to the outer product matrix in step 2. In here, the outer product matrix is NxN matrix. N=(M+1).2^(K-1) where K, M are any integers.

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