سوال ۱۹ کنکور ارشد ریاضی ۱۴۰۰

PASSAGE 1 — Number of Steps, Work per Step, and Preconditioning (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 $Ax = b$ quickly if the eigenvalues of A are <u>clustered</u> 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).

Choose and mark the choice having the word closest in meaning to the underlined word "clustered" in paragraph 2.