dlaed6 (l) - Linux Manuals

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

NAME

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

SYNOPSIS

SUBROUTINE DLAED6(
KNITER, ORGATI, RHO, D, Z, FINIT, TAU, INFO )

    
LOGICAL ORGATI

    
INTEGER INFO, KNITER

    
DOUBLE PRECISION FINIT, RHO, TAU

    
DOUBLE PRECISION D( 3 ), Z( 3 )

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)
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.

ARGUMENTS

KNITER (input) INTEGER
Refer to DLAED4 for its significance.
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.
RHO (input) DOUBLE PRECISION
Refer to the equation f(x) above.
D (input) DOUBLE PRECISION array, dimension (3)
D satisfies d(1) < d(2) < d(3).
Z (input) DOUBLE PRECISION array, dimension (3)
Each of the elements in z must be positive.
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).
TAU (output) DOUBLE PRECISION
The root of the equation f(x).
INFO (output) INTEGER
= 0: successful exit
> 0: if INFO = 1, failure to converge

FURTHER DETAILS

30/06/99: Based on contributions by

Ren-Cang Li, Computer Science Division, University of California
at Berkeley, USA
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.

Pages related to dlaed6

  • dlaed6 (3)
  • dlaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
  • dlaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • dlaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
  • dlaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
  • dlaed4 (l) - subroutine compute the I-th updated eigenvalue of a symmetric rank-one modification to a diagonal matrix whose elements are given in the array d, and that D(i) < D(j) for i < j and that RHO > 0
  • dlaed5 (l) - subroutine compute the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix diag( D ) + RHO The diagonal elements in the array D are assumed to satisfy D(i) < D(j) for i < j
  • dlaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • dlaed8 (l) - merges the two sets of eigenvalues together into a single sorted set
  • dlaed9 (l) - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
  • dlaeda (l) - computes the Z vector corresponding to the merge step in the CURLVLth step of the merge process with TLVLS steps for the CURPBMth problem