سوال ۱۸ کنکور ارشد ریاضی ۱۴۰۲
PASSAGE 2 (excerpt, paragraph 2):
"We shall see that the number of steps required for convergence to a satisfactory precision typically depends on spectral properties of the matrix A, if the word "spectral" is interpreted broadly. For example, the conjugate gradient iteration is guaranteed to solve a hermitian positive definite system quickly if the eigenvalues of A are clustered well away from the origin. Similarly, the Lanczos iteration is guaranteed to compute certain eigenvalues of a real hermitian matrix quickly if those eigenvalues are well separated from the rest of the spectrum (and if the initial vector that starts the iteration is suitably generic)."
What does the underlined word "spectrum" in paragraph 2 mean?
پاسخ صحیح: گزینهٔ B — extent
In the sentence, certain eigenvalues must be "well separated from the rest of the spectrum" — i.e. from the whole range/set of remaining eigenvalues. …
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