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

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

10       SUBROUTINE DLARRK( 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           DOUBLE         PRECISION PIVMIN, RELTOL, GL, GU, W, WERR
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18           DOUBLE         PRECISION D( * ), E2( * )
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PURPOSE

21       DLARRK computes one eigenvalue of a symmetric tridiagonal matrix  T  to
22       suitable accuracy. This is an auxiliary code to be called from DSTEMR.
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) DOUBLE PRECISION
39               GU      (input) DOUBLE PRECISION An upper and a lower bound  on
40               the eigenvalue.
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42       D       (input) DOUBLE PRECISION array, dimension (N)
43               The n diagonal elements of the tridiagonal matrix T.
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45       E2      (input) DOUBLE PRECISION 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) DOUBLE PRECISION
50               The minimum pivot allowed in the Sturm sequence for T.
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52       RELTOL  (input) DOUBLE PRECISION
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) DOUBLE PRECISION
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61       WERR    (output) DOUBLE PRECISION
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   DOUBLE PRECISION, default = 2
71               A "fudge factor" to widen the Gershgorin intervals.
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75 LAPACK auxiliary routine (versionNo3v.e2m)ber 2008                       DLARRK(1)