laed6 - laed6: D&C step: secular equation Newton step

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subroutinedlaed6(integerkniter,logicalorgati,doubleprecisionrho,doubleprecision,dimension(3)d,doubleprecision,dimension(3)z,doubleprecisionfinit,doubleprecisiontau,integerinfo)DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. 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 It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) 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. ParametersKNITER KNITER is INTEGER Refer to DLAED4 for its significance. ORGATI ORGATI is 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. RHO RHO is DOUBLE PRECISION Refer to the equation f(x) above. D D is DOUBLE PRECISION array, dimension (3) D satisfies d(1) < d(2) < d(3). Z Z is DOUBLE PRECISION array, dimension (3) Each of the elements in z must be positive. FINIT FINIT is 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). TAU TAU is DOUBLE PRECISION The root of the equation f(x). INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, failure to converge Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA subroutineslaed6(integerkniter,logicalorgati,realrho,real,dimension(3)d,real,dimension(3)z,realfinit,realtau,integerinfo)SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation. Purpose: SLAED6 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 It is assumed that if ORGATI = .true. the root is between d(2) and d(3); otherwise it is between d(1) and d(2) This routine will be called by SLAED4 when necessary. In most cases, the root sought is the smallest in magnitude, though it might not be in some extremely rare situations. ParametersKNITER KNITER is INTEGER Refer to SLAED4 for its significance. ORGATI ORGATI is 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 SLAED4 for further details. RHO RHO is REAL Refer to the equation f(x) above. D D is REAL array, dimension (3) D satisfies d(1) < d(2) < d(3). Z Z is REAL array, dimension (3) Each of the elements in z must be positive. FINIT FINIT is REAL The value of f at 0. It is more accurate than the one evaluated inside this routine (if someone wants to do so). TAU TAU is REAL The root of the equation f(x). INFO INFO is INTEGER = 0: successful exit > 0: if INFO = 1, failure to converge Author Univ. of Tennessee Univ. of California Berkeley Univ. of Colorado Denver NAG Ltd. FurtherDetails: 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. Contributors: Ren-Cang Li, Computer Science Division, University of California at Berkeley, USA

laed6 - laed6: D&C step: secular equation Newton step

Functions subroutine dlaed6 (kniter, orgati, rho, d, z, finit, tau, info) DLAED6 used by DSTEDC. Computes one Newton step in solution of the secular equation. subroutine slaed6 (kniter, orgati, rho, d, z, finit, tau, info) SLAED6 used by SSTEDC. Computes one Newton step in solution of the secular equation.