سوال ۱۷ کنکور ارشد ریاضی ۱۴۰۲
PASSAGE 2 (excerpt):
"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..."
17- The conjugate gradient iterative method for solving certain linear systems ----------.
پاسخ صحیح: گزینهٔ A — is fast if the eigenvalues of the coefficient matrix spread away from the origin
The deciding line (paragraph 2): "the conjugate gradient iteration is guaranteed to solve a hermitian positive definite system **quickly if the …
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