# Matrix Eigensystem Routines — EISPACK Guide by B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y.

By B.T. Smith, J.M. Boyle, J.J. Dongarra, B.S. Garbow, Y. Ikebe, V.C. Klema, C.B. Moler

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Example text

20 ALL EIGENVALUES OF A SPECIAL REAL TRiDIAGONAL MATRIX A real tridiagonal matrix of order N which, although not symmetric, has the property that products of pairs of corresponding off-diagonal elements are all non-negative, can be presented to EISPACK as a threecolumn array. The subdiagonal elements are stored in the last N-I positions of the first column, the diagonal elements in the second column, and the superdiagonal elements in the first N-I positions of the third column. The first element in the first column and the last element in the third column are arbitrary.

Setting it to zero or calling EISPAC without supplying it causes the use of a default value suitable for most matrices. 3 and in the BISECT and EISPAC documents. Upon completion of the path, M is set to the number of eigenvalues determined to lie in the interval defined by RLB and RUB and, provided M ! ~ , the eigenvalues are in ascending order in W and their corresponding (non-orthonormal) eigenvectors are in the first M columns of Z. Note that, should the computed M be greater than MM, BISECT sets IERR non-zero and does not compute any eigenvalues.

ERR,fv4,fv5,fv6,fv7,fvS) IF (IERR ~NE. 0) GO TO 99999 CALL HTRIBK(NM,N,AR,AI ,fml ,M,ZR, ZI) or, using EISPAC: CALL EISPAC(I~M,N,MATRIX('COMPLEX',AR,AI,'HERMITIANI), VALUES(W,MM,M,RLB,RUB),VECTOR(ZR,ZI)) The parameter EPSI is used to control the accuracy of the eigenvalue computation° Setting it to zero or calling EISPAC without supplying it causes the use of a default value suitable for most matrices. 3 and in the BISECT and EISPAC documents~ Upon completion of the path, M is set to the number of eigenvalues determined to lie in the interval defined by RLB and RUB and, provided M !

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