1SLARRK(1)           LAPACK auxiliary routine (version 3.2)           SLARRK(1)
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NAME

6       SLARRK - computes one eigenvalue of a symmetric tridiagonal matrix T to
7       suitable accuracy
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SYNOPSIS

10       SUBROUTINE SLARRK( N, IW, GL, GU, D, E2, PIVMIN, RELTOL, W, WERR, INFO)
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12           IMPLICIT       NONE
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14           INTEGER        INFO, IW, N
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16           REAL           PIVMIN, RELTOL, GL, GU, W, WERR
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18           REAL           D( * ), E2( * )
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PURPOSE

21       SLARRK computes one eigenvalue of a symmetric tridiagonal matrix  T  to
22       suitable accuracy. This is an auxiliary code to be called from SSTEMR.
23       To avoid overflow, the matrix must be scaled so that its
24       largest element is no greater than overflow**(1/2) *
25       underflow**(1/4) in absolute value, and for greatest
26       accuracy, it should not be much smaller than that.
27       See  W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix",
28       Report CS41, Computer Science Dept., Stanford
29       University, July 21, 1966.
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ARGUMENTS

32       N       (input) INTEGER
33               The order of the tridiagonal matrix T.  N >= 0.
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35       IW      (input) INTEGER
36               The index of the eigenvalues to be returned.
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38       GL      (input) REAL
39               GU      (input) REAL An upper and a lower bound on  the  eigen‐
40               value.
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42       D       (input) REAL             array, dimension (N)
43               The n diagonal elements of the tridiagonal matrix T.
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45       E2      (input) REAL             array, dimension (N-1)
46               The  (n-1)  squared  off-diagonal  elements  of the tridiagonal
47               matrix T.
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49       PIVMIN  (input) REAL
50               The minimum pivot allowed in the Sturm sequence for T.
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52       RELTOL  (input) REAL
53               The minimum relative width of an interval.  When an interval is
54               narrower  than RELTOL times the larger (in magnitude) endpoint,
55               then it is considered to  be  sufficiently  small,  i.e.,  con‐
56               verged.   Note:  this  should  always be at least radix*machine
57               epsilon.
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59       W       (output) REAL
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61       WERR    (output) REAL
62               The error bound on the corresponding  eigenvalue  approximation
63               in W.
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65       INFO    (output) INTEGER
66               = 0:       Eigenvalue converged
67               = -1:      Eigenvalue did NOT converge
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PARAMETERS

70       FUDGE   REAL            , default = 2
71               A "fudge factor" to widen the Gershgorin intervals.
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75 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       SLARRK(1)