Tridiagonal Matrix with subdiagonal and main diagonal is also matrix

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Mücahit Özalp 2021-5-12

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评论： Matt J 2021-5-14

I have two matrices A and B. I want A to be main diagonal and B to be my subdiagonals. How do I create such a matrix? By the way sizes of A and B changes but they are square matrices.

Specifically, a1=4,b1=-1

A =diag(a1*ones(1,N-1)) + diag(b1*ones(1,N-2),1) + diag(b1*ones(1,N-2),-1)

B=(-1)*eye(N-1)

These are my A and B matrices. I need to define a (N-1)*(N-1) times (N-1)*(N-1) matrix . For example for N=1000 or N=5000 I should be able to change the N value.

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Mücahit Özalp 2021-5-14

编辑：Mücahit Özalp 2021-5-14

@Matt JIt's me again now I can form the matrix for N=5000 but I need to evaluate its smallest 10 eigenvalues using E=eigs(D,10,'smallestabs'); I get out of memory error. Is there a way to solve that.

Matt J 2021-5-14

I don't think so, but if you post a new question on it (ideally with a demo), others on the forum may have some thoughts.

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采纳的回答

Matt J 2021-5-12

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此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/828250-tridiagonal-matrix-with-subdiagonal-and-main-diagonal-is-also-matrix#answer_698365

编辑：Matt J 2021-5-12

So, you want a block Toeplitz matrix?

N = 5;
A =diag([7 4 4]);
B=[8 8 10; 2 5 2; 10 8 7];
C=zeros(3);
blocks={C,B,A};
result=cell2mat(blocks( toeplitz(1+[2,1,zeros(1,N-2)])  ))
result = 15×15
     7     0     0     8     8    10     0     0     0     0     0     0     0     0     0
     0     4     0     2     5     2     0     0     0     0     0     0     0     0     0
     0     0     4    10     8     7     0     0     0     0     0     0     0     0     0
     8     8    10     7     0     0     8     8    10     0     0     0     0     0     0
     2     5     2     0     4     0     2     5     2     0     0     0     0     0     0
    10     8     7     0     0     4    10     8     7     0     0     0     0     0     0
     0     0     0     8     8    10     7     0     0     8     8    10     0     0     0
     0     0     0     2     5     2     0     4     0     2     5     2     0     0     0
     0     0     0    10     8     7     0     0     4    10     8     7     0     0     0
     0     0     0     0     0     0     8     8    10     7     0     0     8     8    10

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Matt J 2021-5-12

N = 1000;
a1=4;b1=-1; 
A =diag(a1*ones(1,N-1)) + diag(b1*ones(1,N-2),1) + diag(b1*ones(1,N-2),-1);
B=(-1)*speye(N-1) ;
C=sparse(N-1,N-1);
blocks={C,B,sparse(A)};
result=cell2mat(blocks( toeplitz(1+[2,1,zeros(1,N-3)])  ));
whos result
  Name             Size                    Bytes  Class     Attributes

  result      998001x998001            103680256  double    sparse    