# Questions tagged [tridiagonal-matrices]

Relating to all $n\times n$ matrices $(A)$ with the property $A_{i,j}=0$ if $|j-i|>1$

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### What is meant by tridiagonal linear equation system?

I have to implement the SOR (Successive Over-Relaxation) method, using sparse matrices, to find the solution vector of these linear equations systems (for quite huge matrices): What does that tridiag(...
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### Inverse of a symmetric tridiagonal matrix

I have a symmetric $n\times n$ matrix $\mathbb A$ with entries: $$A_{ij} = (a_i + a_{i-1})\delta_{ij} - a_i\delta_{i,j-1}-a_{j}\delta_{i-1,j}$$ where $a_0,\dots,a_n$ are given positive numbers. Is ...
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### Eigenpairs of a sparse symmetric block tridiagonal matrix with diagonal blocks on the outer diagonals

I'm looking at methods to find the eigenpairs of symmetric block tridiagonal matrices, with sparse blocks on the main diagonal and diagonal blocks on the outer diagonals. Has any research been done on ...
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### Can a symmetric positive definite tridiagonal matrix have a zero coefficient on its diagonal?

I'm investigating the Parallel Cyclic Reduction algorithm (Fast Tridiagonal Solvers on the GPU) in the case of positive definite tridiagonal matrices and I'm wondering whether a 0 can appear on the ...
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### What is the rank of $B$?

Let $A=(a_{ij})$ be the square matrix of size $2018$ defined by $$a_{ij} = \begin{cases} 2 & \text{if } i+1=j\\ \frac{1}{3} & \text{if } i =j+1\\ 0 & \text{otherwise}\end{cases}$$ ...
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### Using Cholesky decomposition to solve a system of equaions $A^TAx=b$

I am looking for a way to use $LL^T$ decomposition of a tridiagonal and symmetric positive definite $n$ by $n$ matrix $A$ to solve $$A^TAx=b.$$ In this case, thanks to $A$ being symmetric, the ...
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### Inversion of a Tridiagonal Matrices and Recurrence equation

I want to find an inverse of an infinite tridiagonal matrix: $A_{m,n} = (\delta_{m,n} (n-1+\Delta) + s(\sqrt{n} \delta_{m+1,n} + \sqrt{m} \delta_{m,n+1}))_{m,n}$ where $\Delta$ and $s$ are real ...
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### Generating a random tridiagonal symmetric positive definite matrix

I am looking for a way to generate random tridiagonal symmetric positive definite matrices in Matlab. I need to be able to generate a matrix of specific size (any number between 1-101). Does anybody ...
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### Why dont we use Given's method to reduce a symmetric matrix to diagonal form rather than tridiagonal form, and why is tridiagonal form desirable?

I've been searching for a while trying to understand why we use Givens method (and householders method) to reduce a symmetric matrix to tri-diagonal form instead of using these methods to reduce a ...
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### Eigenvectors of a tridiagonal stochastic matrix

I'm looking for the eigenvectors of this matrix: \begin{equation} \nonumber M = \frac{1}{N} \left( \begin{array}{ccccccccc} 0 & 1 &&&&&&&\\ N & 0 & 2&&...