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Which of the following functions are sometimes ill-conditioned? f(x) = sqrt(x), assuming x > 0 f(x) = log(x), assuming x>0 O f(b) = A^{-1} b, where A is a positive definite matrix, b is a vector

Which of the following functions are sometimes ill-conditioned? f(x) = sqrt(x), assuming x > 0 f(x) = log(x), assuming x>0 O f(b) = A^{-1} b, where A is a positive definite matrix, b is a vector

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Which of the following functions are sometimes ill-conditioned? f(x) = sqrt(x), assuming x > 0 f(x) = log(x), assuming x>0 f(b) = A^{-1} b, where A is a positive definite matrix, b is a vector O f(x) = x-1000 f(x) = x/1000 f(x) = sin(x) f(x) = Ax, where A is a nonsingular matrix, x is a vector f(x) = (1 + x/n)^n, where n is a positive integer, assuming |x| < 1 f(b) = A^{-1} b, where A is a nonsingular matrix, b is a vector f(x) = cos(x) f(x) = exp(x), assuming |x| < 1
Transcribed Image Text:Which of the following functions are sometimes ill-conditioned? f(x) = sqrt(x), assuming x > 0 f(x) = log(x), assuming x>0 f(b) = A^{-1} b, where A is a positive definite matrix, b is a vector O f(x) = x-1000 f(x) = x/1000 f(x) = sin(x) f(x) = Ax, where A is a nonsingular matrix, x is a vector f(x) = (1 + x/n)^n, where n is a positive integer, assuming |x| < 1 f(b) = A^{-1} b, where A is a nonsingular matrix, b is a vector f(x) = cos(x) f(x) = exp(x), assuming |x| < 1
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