.TH DLAED6 1 "February 2007" " LAPACK routine (version 3.1.1) " " LAPACK routine (version 3.1.1) " .SH NAME DLAED6 - the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x It is assumed that if ORGATI = .true .SH SYNOPSIS .TP 19 SUBROUTINE DLAED6( KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO ) .TP 19 .ti +4 LOGICAL ORGATI .TP 19 .ti +4 INTEGER INFO, KNITER .TP 19 .ti +4 DOUBLE PRECISION FINIT, RHO, TAU .TP 19 .ti +4 DOUBLE PRECISION D( 3 ), Z( 3 ) .SH PURPOSE DLAED6 computes the positive or negative root (closest to the origin) of z(1) z(2) z(3) f(x) = rho + --------- + ---------- + --------- d(1)-x d(2)-x d(3)-x otherwise it is between d(1) and d(2) .br This routine will be called by DLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations. .br .SH ARGUMENTS .TP 13 KNITER (input) INTEGER Refer to DLAED4 for its significance. .TP 13 ORGATI (input) LOGICAL If ORGATI is true, the needed root is between d(2) and d(3); otherwise it is between d(1) and d(2). See DLAED4 for further details. .TP 13 RHO (input) DOUBLE PRECISION Refer to the equation f(x) above. .TP 13 D (input) DOUBLE PRECISION array, dimension (3) D satisfies d(1) < d(2) < d(3). .TP 13 Z (input) DOUBLE PRECISION array, dimension (3) Each of the elements in z must be positive. .TP 13 FINIT (input) DOUBLE PRECISION The value of f at 0. It is more accurate than the one evaluated inside this routine (if someone wants to do so). .TP 13 TAU (output) DOUBLE PRECISION The root of the equation f(x). .TP 13 INFO (output) INTEGER = 0: successful exit .br > 0: if INFO = 1, failure to converge .SH FURTHER DETAILS 30/06/99: Based on contributions by .br Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA .br 10/02/03: This version has a few statements commented out for thread safety (machine parameters are computed on each entry). SJH. 05/10/06: Modified from a new version of Ren-Cang Li, use Gragg-Thornton-Warner cubic convergent scheme for better stability.