laed5(3) LAPACK laed5(3)

laed5 - laed5: D&C step: secular equation, 2x2


subroutine dlaed5 (i, d, z, delta, rho, dlam)
DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation. subroutine slaed5 (i, d, z, delta, rho, dlam)
SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

DLAED5 used by DSTEDC. Solves the 2-by-2 secular equation.

Purpose:

 This subroutine computes the I-th eigenvalue of a symmetric rank-one
 modification of a 2-by-2 diagonal matrix
            diag( D )  +  RHO * Z * transpose(Z) .
 The diagonal elements in the array D are assumed to satisfy
            D(i) < D(j)  for  i < j .
 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one.

Parameters

I 

          I is INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.

D

          D is DOUBLE PRECISION array, dimension (2)
         The original eigenvalues.  We assume D(1) < D(2).

Z

          Z is DOUBLE PRECISION array, dimension (2)
         The components of the updating vector.

DELTA

          DELTA is DOUBLE PRECISION array, dimension (2)
         The vector DELTA contains the information necessary
         to construct the eigenvectors.

RHO

          RHO is DOUBLE PRECISION
         The scalar in the symmetric updating formula.

DLAM

          DLAM is DOUBLE PRECISION
         The computed lambda_I, the I-th updated eigenvalue.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

SLAED5 used by SSTEDC. Solves the 2-by-2 secular equation.

Purpose:

 This subroutine computes the I-th eigenvalue of a symmetric rank-one
 modification of a 2-by-2 diagonal matrix
            diag( D )  +  RHO * Z * transpose(Z) .
 The diagonal elements in the array D are assumed to satisfy
            D(i) < D(j)  for  i < j .
 We also assume RHO > 0 and that the Euclidean norm of the vector
 Z is one.

Parameters

I 

          I is INTEGER
         The index of the eigenvalue to be computed.  I = 1 or I = 2.

D

          D is REAL array, dimension (2)
         The original eigenvalues.  We assume D(1) < D(2).

Z

          Z is REAL array, dimension (2)
         The components of the updating vector.

DELTA

          DELTA is REAL array, dimension (2)
         The vector DELTA contains the information necessary
         to construct the eigenvectors.

RHO

          RHO is REAL
         The scalar in the symmetric updating formula.

DLAM

          DLAM is REAL
         The computed lambda_I, the I-th updated eigenvalue.

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Contributors:

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

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