Description

[xv,lmb,iresult] = sptarn(A,B,lb,ub,spd,tolconv,jmax,maxmul) finds eigenvalues of the pencil (A – λB)x = 0 in interval [lb,ub]. (A matrix of linear polynomials A ij – λB ij , A – λB, is called a pencil.)

A and B are sparse matrices. lb and ub are lower and upper bounds for eigenvalues to be sought. We may have lb = -inf if all eigenvalues to the left of ub are sought, and rb = inf if all eigenvalues to the right of lb are sought. One of lb and ub must be finite. A narrower interval makes the algorithm faster. In the complex case, the real parts of lmb are compared to lb and ub .

xv are eigenvectors, ordered so that norm(a*xv-b*xv*diag(lmb)) is small. lmb is the sorted eigenvalues. If iresult >= 0 the algorithm succeeded, and all eigenvalues in the intervals have been found. If iresult<0 the algorithm has not yet been successful, there may be more eigenvalues—try with a smaller interval.

spd is 1 if the pencil is known to be symmetric positive definite (default 0 ).

tolconv is the expected relative accuracy. Default is 100*eps , where eps is the machine precision.

jmax is the maximum number of basis vectors. The algorithm needs jmax*n working space so a small value may be justified on a small computer, otherwise let it be the default value jmax = 100 . Normally the algorithm stops earlier when enough eigenvalues have converged.