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A tridiagonal matrix is a band matrix that has nonzero elements only on the main diagonal, the first diagonal below this, and the first diagonal above the main diagonal.
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Upper Bounds on the Largest Eigenvalue of Jacobi Matrices
Suppose I have a symmetric tridiagonal (Jacobi) matrix in the following form:
$ \begin{pmatrix}
1 & a_{1} & 0 & ... & 0 \\\
a_{1} & 1 & a_{2} & & ... \\\
0 & a_{2} & 1 & ... & 0 \\\
... & & ... & …