By Roland Ganbler
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Within the Seventies, whereas their contemporaries have been protesting the pc as a device of dehumanization and oppression, a motley selection of university dropouts, hippies, and electronics lovers have been engaged in anything even more subversive. captivated with the belief of having computing device energy into their very own arms, they introduced from their garages a hobbyist circulation that grew into an undefined, and eventually a social and technological revolution.
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The algorithm used in EISPACK determines two unitary matrices Q and Z such that QAZ and QBZ are both upper triangular. j and Bj are simply the diagonal elements of the two triangular matrices, and it is these quantities which are returned by the subroutine. /B.. JJ there is more in the individual ~. and B. than there is in the ratios ] 3 The errors in aj and $. are all about the same absolute size, J namely the size of the errors in the input data (or of roundoff errors in the computation). 3-3 the same size as the original matrix elements, determined by the data and the computation.
1-16 The array storage required to execute this path is 3N 2 + 3N working precision words. However, for this particular path the eigenvectors can overwrite the A matrix if the same array parameter is used for both A and Z, thereby reducing the storage required to 2N 2 + 3N working precision words. 0 seconds for sample systems of order I0, 20, 40, and 80 respectively. 3 of [I0]. 2 of this volume. 1~6 ALL EIGENVALUES OF A GENEP~IIZED REAL SYMMETRIC MATRIX SYSTEM The real generalized eigenproblem Az = hBz is further characterized as symmetric if both A and B are symmetric and B is positive definite (all positive eigenvalues).
NE. 0) GO TO 99999 CALL TRBAKI(NM,N,A,fv2,M,Z) CALL REBAK(NM,N,B,fv9,M,Z) or, using EISPAC: CALL EISPAC(NM,N,MATA('REAL',A,'SYMMETRIC'),MATB('REAL',B,'SYMMETRIC', 'POSITIVE DEFINITE'),VALUES(W,MM,M,RLB,RUB),VECTOR(Z)) The parameter computation. EPSI is used to control the accuracy of the eigenvalue Setting it to zero or calling EISPAC without supplying causes the use of a default value suitable for most matrices. 3 and in the BISECT and EISPAC documents. 1-20 number of eigenvalues determined to lie in the interval defined by RLB and RUB and, provided M !