Consider the function f(x)=x+1- for large , say 10. (a) Use the concept of condition...

  

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Consider the function f(x)=√x+1-√ for "large" , say ≈ 10¹. (a) Use the concept of condition numbers to show that the problem of evaluating f(x) for "large" z is well-conditioned. (b) Consider the following algorithm (implemented by matlab script) for computing f(10¹): 20 x1 x2 = x3 x4 = = 10000; =x0+ 1; sqrt(x1); sqrt(x0); x2 - x3; Explain why this algorithm is numerically unstable. (c) Design a stable algorithm to calculate f(10¹). Consider the function f(x)=√x+1-√ for "large" , say ≈ 10¹. (a) Use the concept of condition numbers to show that the problem of evaluating f(x) for "large" z is well-conditioned. (b) Consider the following algorithm (implemented by matlab script) for computing f(10¹): 20 x1 x2 = x3 x4 = = 10000; =x0+ 1; sqrt(x1); sqrt(x0); x2 - x3; Explain why this algorithm is numerically unstable. (c) Design a stable algorithm to calculate f(10¹).

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