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Let f E C4([1, 9]). Consider the following finite difference approximation f(2) = f(x+2h)-2f(x)+f(x-2h) 4h2 + 0 (h ? ) . Then . The roundoff
Let f E C4([1, 9]). Consider the following finite difference approximation f"(2) = f(x+2h)-2f(x)+f(x-2h) 4h2 + 0 (h ? ) . Then . The roundoff error is O ( E ha ), where & is the relative machine precision. . The truncation error is O(h). . The optimal step size is h* = O(Ec). . The optimal total error is E* = O(ed). Here we have a = Number b = Number C = Number d = Number When using double precision floating point arithmetic, we have the estimates (give your answers to 2 significant figures) h* ~ Number E* ~ Number
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