Write any two differences between direct method and iterative method. Derive theorder of convergence of following iterative method.xnaXn+1 =+ converges to a√2.—2 xn

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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(Babylonian Method). All numerical answers should be rounded to 6-digit floating-point numbers. (0) If A > 0 is a positive number, then given a real number xo, the sequence (xn) defined recursively by where n > 0 is a natural number, converges to √A, that is, provided that the initial term xo is chosen 'not too badly'. In practice, calculation of terms xn is carried out till this or that stopping criterion is triggered. (i) Let (xn) be the sequence defined recursively by (ii) Generate the terms and x0 = 94 (as it could be guessed from part (0), the sequence (xn) converges to √946). x() = Xn+1= = = (x++) ₁ (n ≥ 0), x1 = x2 = of the sequence (xn) till you find the term x N satisfying the condition x3 = fl(xN) = fl(xN-I (our stopping criterion), where fl(z) denotes the result of rounding of a real number z to a 6-digit floating-point number. Along the way, once the k-th term xk is generated, enter in the corresponding input field the result fl(xk) of rounding of xk to a 6-digit…
A loan L is repaid using increasing payments. The first payment, made at t = 1, is of amount 200,and each subsequent payment increases by a factor of (1.05), with the last payment at t = 20. However, att = 10, the borrower decides to make an additional payment of X, which allow him to halve the size of theremaining payments (t = 11, ..., 20). Determine L and X if the effective interest is 8%.
Suppose we want to obtain a root of x4 - x - 10 = 0. We can rewrite it as x = √√x+10. If we use the fixed-point iteration method on f(x) = √√x+10 to construct the sequence {x}, with xo = 1.5, to estimate a root of x-x-10 = 0, then the smallest value of n so that x, estimates the said root to three significant digits is
Let a be a nonzero real number. For any xo satisfying 0 < x < 2/a, the recursive sequence defined by Xn+1= xn (2 Axn) — converges to some limiting value. (a) Find the value. (b) What is the order of convergence? (c) Find the asymptotic error constant.
Solve for the interval of convergence (see picture).
Suppose we want to obtain a root of x-x-10 = 0. We can rewrite it as x = √√x + 10. If we use the fixed-point iteration method on f(x)=√√x + 10 to construct the sequence {x}, with xo = 1.5, to estimate a root of x-x-10 = 0, then the smallest value of n so that x, estimates the said root to three significant digits is Blank 1. Blank 1 Add your answer
2am-1 +1 is non-homogeneous because of the additional mple, an = stant 1. There are general methods of solving such things, but we I not consider them here, other than through the use of telescoping or cation described above. EXERCISES beginning 3,5,11,21,43,85. Then give a recursive definition for the sequence. Finally, use the characteristic root technique to find a closed formula for the sequence. Find the next two terms in (an)n>o begi . Consider the seauences 2 5 12 29 70 169 408 1229 70 169 408 with a-
SOLVE STEP BY STEP IN DIGITAL FORMAT 5. Consider the sequence of functions {f(x)}n given by f(x) Show that this sequence of functions is pointwise convergent and for all x. = for xE[0,1] and 0 otherwise. n converges to the function f(x)=0
ADVANCED MATH (No Long Explanation needed. Rate will be given) Choose "DIVERGENT OR CONVERGENT"
can you please show step by step on how to solve this especilaly the induction step so i can understand how to approach similaar problems later on please?
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Write any two differences between direct method and iterative method. Derive the order of convergence of following iterative method. a Xn Xn+1 = 2² +₁ converges to a√2. 2 xn