A problem is ill-conditioned if its solution is highly sensitive to small change

Question

A problem is ill-conditioned if its solution is highly sensitive to small changes in the input data. True or False? Using higher-precision arithmetic will make an ill-conditioned problem better conditioned. True or False? If two real numbers are exactly representable as floating-point numbers on a finite precision machine, then so is their product. True or False? Consider the sum S = 1/x + 1 + 1/x - 1. X notequalto 1. For what range of values is it difficult to compute S accurately in a finite-precision system? How will you rearrange the terms in S so that the difficulty disappears? In a finite-precision system with UFL = 10^-40, which of the following operations will incur an underflow? Squareroot a^2 + b^2, with a = 1, b = 10^-25. Squareroot a^2 + b^2, with a = b = 10^-25. (a times b)/(c times d), with a = 10^-20, b = 10^-25, c = 10^-10, d = 10^-35.

Explanation / Answer

7 ans False. ill-conditioned problem => highcondition number =>–relativechange in solution >>relativechangein input)

7 b ans) False. Conditioning is a characteristic ofthe problem, not the algorithm

7c ans ) true product of floating point is always true

74ans) here we will replace

s= ( x+1+x-1) / x2-1 = 2x /x2-1

genearlly s= (1,-1) are the solutions

will replace in such a way that s should be (1,-1)

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