Consider finding a numerical solution to f(x) = x³ + 10x² – 9 = 0. ising the iterative scheme *k+1 = 9(xk) = k = 0,1, ... Tk + 10' (a) Using an initial guess æ0 = -7, calculate r2 to two decimal places. 12 = Number (b) Theory guarantees that the fixed-point iteration converges to a solution for every initial guess ro greater than what minimum value ( decimal places)? T0 2 Number

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.5: Iterative Methods For Solving Linear Systems
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Consider finding a numerical solution to
f(x) = 23 + 10x² – 9 = 0.
ising the iterative scheme
9
*k+1 = g(x1) =
k = 0,1,...
*k + 10
(a) Using an initial guess ao =-7, calculate xɔ to two decimal places.
22 = Number
(b) Theory guarantees that the fixed-point iteration converges to a solution for every initial guess xo greater than what minimum value (accurate to two
decimal places)?
20 2 Number
Transcribed Image Text:Consider finding a numerical solution to f(x) = 23 + 10x² – 9 = 0. ising the iterative scheme 9 *k+1 = g(x1) = k = 0,1,... *k + 10 (a) Using an initial guess ao =-7, calculate xɔ to two decimal places. 22 = Number (b) Theory guarantees that the fixed-point iteration converges to a solution for every initial guess xo greater than what minimum value (accurate to two decimal places)? 20 2 Number
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