On the other hand, A finite

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On the other hand, A finite **number of eigenvalues** in one spectrum is unknown, q(x) is not uniquely determined by one full spectrum and one partial spectrum.

Iterative projection methods have proven to be very efficient if a small **number of eigenvalues** and eigenvectors are desired.

In ARPACK, the computational work is proportional to n (the size of the matrix is n by n, n = 10 N or 20 N) times ncv (which defines the size of the space to use in finding eigenvectors; we choose ncv to be 4 times the **number of eigenvalues** sought).

Then for any 0 < [epsilon] < [pi], the **number of eigenvalues** of [H.

Neither the one-sided standard nor the two-sided standard extraction is able to compute the required **number of eigenvalues** in the prescribed number of outer iterations (therefore, we omit the number of iterations and the cpu time for these methods).

The **number of eigenvalues** (and eigenvectors) one can compute, from one tridiagonal matrix, is much larger than the number of vectors that one must store in memory.