24 lines
2.1 KiB
Markdown
24 lines
2.1 KiB
Markdown
# Tridiagonal Matrices
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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).
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Common Parameters:
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- jobv — Determines whether to compute eigenvectors (EIGVALUES_V) or only eigenvalues (EIGVALUES_N).
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- range — Specifies the range of computed eigenvalues (BLASRANGE_A, BLASRANGE_V, BLASRANGE_I).
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- lower and upper — Lower and upper bounds for computing a subset of the spectrum.
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- abstol — Absolute error tolerance.
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All functions operate on symmetric tridiagonal matrices and allow selecting the most suitable algorithm depending on performance and accuracy requirements.
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| Function | Action |
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| --- | --- |
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| EigenTridiagonalDC | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function STEVD ). |
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| EigenTridiagonalQR | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function STEV ). |
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| EigenTridiagonalRobust | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the Multiple Relatively Robust Representations, MRRR algorithm (LAPACK function STEVR ). |
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| EigenTridiagonalBisect | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the bisection algorithm (LAPACK function STEVX ). |
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| EigenTridiagonalQL | Compute all eigenvalues of a symmetric tridiagonal matrix using the Pal-Walker-Kahan variant of the QL or QR algorithm (LAPACK function STERF ). |
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| EigenTridiagonalDCQ | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the divide-and-conquer algorithm (LAPACK function STEDC ). |
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| EigenTridiagonalQRQ | Compute eigenvalues and eigenvectors of a symmetric tridiagonal matrix using the QR algorithm (LAPACK function STEQR ). |
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| EigenTridiagonalPosDefQ | Compute eigenvalues and eigenvectors of a symmetric positive definite (положительно определённая) tridiagonal matrix using the QR algorithm (LAPACK function PTEQR ). |
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