# Tridiagonal Matrices

Functions for computing eigenvalues and eigenvectors of symmetric tridiagonal matrices using various algorithms. Each function implements a specific solution method and supports matrix types [double](/en/docs/basis/types/double) and [float](/en/docs/basis/types/double).

Common Parameters:

- jobv — Determines whether to compute eigenvectors (EIGVALUES_V) or only eigenvalues (EIGVALUES_N).
- range — Specifies the range of computed eigenvalues (BLASRANGE_A, BLASRANGE_V, BLASRANGE_I).
- lower and upper — Lower and upper bounds for computing a subset of the spectrum.
- abstol — Absolute error tolerance.

All functions operate on symmetric tridiagonal matrices and allow selecting the most suitable algorithm depending on performance and accuracy requirements.

| Function | Action |
| --- | --- |
| EigenTridiagonalDC | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function  STEVD ). |
| EigenTridiagonalQR | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function  STEV ). |
| EigenTridiagonalRobust | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the Multiple Relatively Robust Representations, MRRR algorithm (LAPACK function  STEVR ). |
| EigenTridiagonalBisect | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the bisection algorithm (LAPACK function  STEVX ). |
| EigenTridiagonalQL | Compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm (LAPACK function  STERF ). |
| EigenTridiagonalDCQ | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function  STEDC ). |
| EigenTridiagonalQRQ | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function  STEQR ). |
| EigenTridiagonalPosDefQ | Compute eigenvalues and eigenvectors of a symmetric positive definite (положительно определённая) tridiagonal matrix using the QR algorithm (LAPACK function  PTEQR ). |