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Tridiagonal Matrix with subdiagonal and main diagonal is also matrix

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Mücahit Özalp
Mücahit Özalp 2021-5-12
Locked: Steven Lord 2024-7-13
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
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
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
Matt J 2021-5-12
编辑：Matt J 2021-5-12
Ran in:
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
Matt J 2021-5-12
Ran in:
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

更多回答（1 个）

Matt J
Matt J 2021-5-12
Ran in:
Here's another way, probably much faster.
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)*eye(N-1);
E0=speye(N);
E1=E0(2:end,1:end-1);
E0=E0(1:end-1,1:end-1);
result=kron(E0,A) + kron(E1,B)+kron(E1.',B);
whos result
Name Size Bytes Class Attributes result 998001x998001 87760160 double sparse

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