# laed6 - Man Page

laed6: D&C step: secular equation Newton step

## Synopsis

### 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.

## Detailed Description

## Function Documentation

### subroutine dlaed6 (integer kniter, logical orgati, double precision rho, double precision, dimension( 3 ) d, double precision, dimension( 3 ) z, double precision finit, double precision tau, integer info)

**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.

**Parameters***KNITER*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.

**Further Details:**

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

Definition at line **139** of file **dlaed6.f**.

### subroutine slaed6 (integer kniter, logical orgati, real rho, real, dimension( 3 ) d, real, dimension( 3 ) z, real finit, real tau, integer info)

**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.

**Parameters***KNITER*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.

**Further Details:**

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

Definition at line **139** of file **slaed6.f**.

## Author

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