1SLARRK(1)           LAPACK auxiliary routine (version 3.1)           SLARRK(1)
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NAME

6       SLARRK - one eigenvalue of a symmetric tridiagonal matrix T to suitable
7       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.
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24       To avoid overflow, the matrix must be scaled so that its
25       largest element is no greater than overflow**(1/2) *
26       underflow**(1/4) in absolute value, and for greatest
27       accuracy, it should not be much smaller than that.
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29       See  W. Kahan "Accurate Eigenvalues of a Symmetric Tridiagonal Matrix",
30       Report CS41, Computer Science Dept., Stanford
31       University, July 21, 1966.
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ARGUMENTS

35       N       (input) INTEGER
36               The order of the tridiagonal matrix T.  N >= 0.
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38       IW      (input) INTEGER
39               The index of the eigenvalues to be returned.
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41       GL      (input) REAL
42               GU      (input) REAL An upper and a lower bound on  the  eigen‐
43               value.
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45       D       (input) REAL             array, dimension (N)
46               The n diagonal elements of the tridiagonal matrix T.
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48       E2      (input) REAL             array, dimension (N-1)
49               The  (n-1)  squared  off-diagonal  elements  of the tridiagonal
50               matrix T.
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52       PIVMIN  (input) REAL
53               The minimum pivot allowed in the Sturm sequence for T.
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55       RELTOL  (input) REAL
56               The minimum relative width of an interval.  When an interval is
57               narrower  than RELTOL times the larger (in magnitude) endpoint,
58               then it is considered to  be  sufficiently  small,  i.e.,  con‐
59               verged.   Note:  this  should  always be at least radix*machine
60               epsilon.
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62       W       (output) REAL
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64       WERR    (output) REAL
65               The error bound on the corresponding  eigenvalue  approximation
66               in W.
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68       INFO    (output) INTEGER
69               = 0:       Eigenvalue converged
70               = -1:      Eigenvalue did NOT converge
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PARAMETERS

73       FUDGE   REAL            , default = 2
74               A "fudge factor" to widen the Gershgorin intervals.
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78 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                       SLARRK(1)