# sstech.f - Man Page

TESTING/EIG/sstech.f

## Synopsis

### Functions/Subroutines

subroutine **sstech** (n, a, b, eig, tol, work, info)**SSTECH**

## Function/Subroutine Documentation

### subroutine sstech (integer n, real, dimension( * ) a, real, dimension( * ) b, real, dimension( * ) eig, real tol, real, dimension( * ) work, integer info)

**SSTECH**

**Purpose:**

Let T be the tridiagonal matrix with diagonal entries A(1) ,..., A(N) and offdiagonal entries B(1) ,..., B(N-1)). SSTECH checks to see if EIG(1) ,..., EIG(N) are indeed accurate eigenvalues of T. It does this by expanding each EIG(I) into an interval [SVD(I) - EPS, SVD(I) + EPS], merging overlapping intervals if any, and using Sturm sequences to count and verify whether each resulting interval has the correct number of eigenvalues (using SSTECT). Here EPS = TOL*MACHEPS*MAXEIG, where MACHEPS is the machine precision and MAXEIG is the absolute value of the largest eigenvalue. If each interval contains the correct number of eigenvalues, INFO = 0 is returned, otherwise INFO is the index of the first eigenvalue in the first bad interval.

**Parameters***N*N is INTEGER The dimension of the tridiagonal matrix T.

*A*A is REAL array, dimension (N) The diagonal entries of the tridiagonal matrix T.

*B*B is REAL array, dimension (N-1) The offdiagonal entries of the tridiagonal matrix T.

*EIG*EIG is REAL array, dimension (N) The purported eigenvalues to be checked.

*TOL*TOL is REAL Error tolerance for checking, a multiple of the machine precision.

*WORK*WORK is REAL array, dimension (N)

*INFO*INFO is INTEGER 0 if the eigenvalues are all correct (to within 1 +- TOL*MACHEPS*MAXEIG) >0 if the interval containing the INFO-th eigenvalue contains the incorrect number of eigenvalues.

**Author**Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line **100** of file **sstech.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sstech(3) is an alias of sstech.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK