?sterf

Developer Reference for Intel® oneAPI Math Kernel Library for C

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ID 766684

Date 4/28/2026

Version

Public

?sterf

Computes all eigenvalues of a real symmetric tridiagonal matrix using QR algorithm.

Syntax

lapack_intLAPACKE_ssterf ( lapack_intn , float*d , float*e );

lapack_intLAPACKE_dsterf ( lapack_intn , double*d , double*e );

Include Files

mkl.h

Description

ssterf dsterf sterf

The routine computes all the eigenvalues of a real symmetric tridiagonal matrix T (which can be obtained by reducing a symmetric or Hermitian matrix to tridiagonal form). The routine uses a square-root-free variant of the QR algorithm.

If you need not only the eigenvalues but also the eigenvectors, call steqr .

Input Parameters

n

The order of the matrix T ( n≥ 0 ).

d , e

REAL for ssterf DOUBLE PRECISION for dsterf . Arrays:

d contains the diagonal elements of T .

The dimension of d must be at least max(1, n ).

e contains the off-diagonal elements of T .

The dimension of e must be at least max(1, n -1).

Output Parameters

d: The n eigenvalues in ascending order, unless info > 0. See also info .
e: On exit, the array is overwritten; see info .

Return Values

This function returns a value info .

If info=0 , the execution is successful.
If info = i , the algorithm failed to find all the eigenvalues after 30 n iterations:
i off-diagonal elements have not converged to zero. On exit, d and e contain, respectively, the diagonal and off-diagonal elements of a tridiagonal matrix orthogonally similar to T .
If info = -i , the i -th parameter had an illegal value.

Fortran 95 Interface Notes

There exist FORTRAN 77 and FORTRAN 95 interfaces for this routine. See the Intel® oneMKL Fortran Developer Reference for details.

Application Notes

The computed eigenvalues and eigenvectors are exact for a matrix \(T+E\) such that \(||E||_{2} = O(\varepsilon) ||T||_{2}\) , where \(\varepsilon\) is the machine precision.

If λ _i is an exact eigenvalue, and m_i is the corresponding computed value, then

\(|\mu i - \lambda i| \leq c(n) \varepsilon ||T||_{2}\)

where c(n) is a modestly increasing function of n .

The total number of floating-point operations depends on how rapidly the algorithm converges. Typically, it is about \(14n^{2}\) .

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Developer Reference for Intel® oneAPI Math Kernel Library for C

?sterf

Syntax

Include Files

Description

Input Parameters

Output Parameters

Return Values

Fortran 95 Interface Notes

Application Notes