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Cyclic Triadiagonal Matrix | PDF | Matrix (Mathematics) | Factorization

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$\notag A = \begin{bmatrix} d_1 & e_1 & & &\\ c_2 & d_2 & e_2 & &\\ & c_3 & \ddots & \ddots &\\ & & \ddots & \ddots & e_{n-1}\\ & & & c_n & d_n \end{bmatrix} \in\mathbb{C}^{n\times n}.$

What Is a Tridiagonal Matrix? – Nick Higham

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$\notag T_5 = \left[ \begin{array}{@{}*{4}{r@{\mskip10mu}}r} 4 & -1 & & & \\ -1 & 4 & -1 & & \\ & -1 & 4 & -1 & \\ & & -1 & 4 & -1 \\ & & & -1 & 4 \end{array}\right].$

What Is a Tridiagonal Matrix? – Nick Higham

$\notag L = \begin{bmatrix} 1 & & & & \\ \ell_2 & 1 & & & \\ & \ell_3 & 1 & & \\ & & \ddots & \ddots & \\ & & & \ell_n & 1 \end{bmatrix}, \quad U = \begin{bmatrix} u_1 & e_1 & & & \\ & u_2 & e_2 & & \\ & & \ddots & \ddots & \\ & & & \ddots & e_{n-1}\\ & & & & u_n \end{bmatrix}. \qquad (3)$

What Is a Tridiagonal Matrix? – Nick Higham

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$\notag T_5(-1,3,-1)^{-1} = \left[\begin{array}{rrrrr} 3 & -1 & 0 & 0 & 0\\ -1 & 3 & -1 & 0 & 0\\ 0 & -1 & 3 & -1 & 0\\ 0 & 0 & -1 & 3 & -1\\ 0 & 0 & 0 & -1 & 3 \end{array}\right]^{-1} = \frac{1}{144} \left[\begin{array}{ccccc} 55 & 21 & 8 & 3 & 1 \\ 21 & 63 & 24 & 9 & 3 \\ 8 & 24 & 64 & 24 & 8 \\ 3 & 9 & 24 & 63 & 21\\ 1 & 3 & 8 & 21 & 55 \end{array}\right].$

What Is a Tridiagonal Matrix? – Nick Higham

What Is a Tridiagonal Matrix? Breaking Down the Basics - Quant Matter

Tridiagonal Matrix -- from Wolfram MathWorld

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$\notag \begin{aligned} d_i &= \frac{n+1}{2} - i = d_{n-i+1}, \quad i = 1:n/2, \qquad d_{(n+1)/2} = 0 \quad \mathrm{if}~n~\mathrm{is~odd}, \\ c_i &= e_{i-1} = 1. \end{aligned}$

What Is a Tridiagonal Matrix? – Nick Higham

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A 9 × 9 tridiagonal matrix. | Download Scientific Diagram

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