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NAME CLAIC1 - apply one step of incremental condition estimation in its simplest version SYNOPSIS SUBROUTINE CLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) INTEGER J, JOB REAL SEST, SESTPR COMPLEX C, GAMMA, S COMPLEX W( J ), X( J ) PURPOSE CLAIC1 applies one step of incremental condition estimation in its simplest version: Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j lower triangular matrix L, such that twonorm(L*x) = sest Then CLAIC1 computes sestpr, s, c such that the vector [ s*x ] xhat = [ c ] is an approximate singular vector of [ L 0 ] Lhat = [ w' gamma ] in the sense that twonorm(Lhat*xhat) = sestpr. Depending on JOB, an estimate for the largest or smallest singular value is computed. Note that [s c]' and sestpr**2 is an eigenpair of the system diag(sest*sest, 0) + [alpha gamma] * [ conjg(alpha) ] [ conjg(gamma) ] where alpha = conjg(x)'*w. ARGUMENTS JOB (input) INTEGER = 1: an estimate for the largest singular value is computed. = 2: an estimate for the smallest singular value is computed. J (input) INTEGER Length of X and W X (input) COMPLEX array, dimension (J) The j-vector x. SEST (input) REAL Estimated singular value of j by j matrix L W (input) COMPLEX array, dimension (J) The j-vector w. GAMMA (input) COMPLEX The diagonal element gamma. SESTPR (output) REAL Estimated singular value of (j+1) by (j+1) matrix Lhat. S (output) COMPLEX Sine needed in forming xhat. C (output) COMPLEX Cosine needed in forming xhat.