slaed5 (l) - Linux Manuals

slaed5: 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

NAME

SLAED5 - 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

SYNOPSIS

SUBROUTINE SLAED5(
I, D, Z, DELTA, RHO, DLAM )

    
INTEGER I

    
REAL DLAM, RHO

    
REAL D( 2 ), DELTA( 2 ), Z( 2 )

PURPOSE

This subroutine computes the I-th eigenvalue of a symmetric rank-one modification of a 2-by-2 diagonal matrix We also assume RHO > 0 and that the Euclidean norm of the vector Z is one.

ARGUMENTS

I (input) INTEGER
The index of the eigenvalue to be computed. I = 1 or I = 2.
D (input) REAL array, dimension (2)
The original eigenvalues. We assume D(1) < D(2).
Z (input) REAL array, dimension (2)
The components of the updating vector.
DELTA (output) REAL array, dimension (2)
The vector DELTA contains the information necessary to construct the eigenvectors.
RHO (input) REAL
The scalar in the symmetric updating formula.
DLAM (output) REAL
The computed lambda_I, the I-th updated eigenvalue.

FURTHER DETAILS

Based on contributions by

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

Pages related to slaed5

  • slaed5 (3)
  • slaed0 (l) - computes all eigenvalues and corresponding eigenvectors of a symmetric tridiagonal matrix using the divide and conquer method
  • slaed1 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • slaed2 (l) - merges the two sets of eigenvalues together into a single sorted set
  • slaed3 (l) - finds the roots of the secular equation, as defined by the values in D, W, and RHO, between 1 and K
  • slaed4 (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
  • slaed6 (l) - 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
  • slaed7 (l) - computes the updated eigensystem of a diagonal matrix after modification by a rank-one symmetric matrix
  • slaed8 (l) - merges the two sets of eigenvalues together into a single sorted set
  • slaed9 (l) - finds the roots of the secular equation, as defined by the values in D, Z, and RHO, between KSTART and KSTOP
  • slaeda (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