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DLAIC1(l)) DLAIC1(l)NAMEDLAIC1 - applie one step of incremental condition estimation in its simplest versionSYNOPSISSUBROUTINE DLAIC1( JOB, J, X, SEST, W, GAMMA, SESTPR, S, C ) INTEGER J, JOB DOUBLE PRECISION C, GAMMA, S, SEST, SESTPR DOUBLE PRECISION W( J ), X( J )PURPOSEDLAIC1 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 DLAIC1 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] * [ alpha ] [ gamma ] where alpha = x'*w.ARGUMENTSJOB (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) DOUBLE PRECISION array, dimension (J) The j-vector x. SEST (input) DOUBLE PRECISION Estimated singular value of j by j matrix L W (input) DOUBLE PRECISION array, dimension (J) The j-vector w. GAMMA (input) DOUBLE PRECISION The diagonal element gamma. SEDTPR (output) DOUBLE PRECISION Estimated singular value of (j+1) by (j+1) matrix Lhat. S (output) DOUBLE PRECISION Sine needed in forming xhat. C (output) DOUBLE PRECISION Cosine needed in forming xhat.LAPACK version 3.015 June 2000 DLAIC1(l)

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