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this is numerical analysis 2. Consider the function f(x) = -21° +1. (a) Calculate the interpolating polynomial pz() for data using the nodes 2o = -1, 11 = 0, 12 = 1. Simplify the polynomial to standard form. Use the error theorem for polynomial interpolation to bound the error f(x) - P2(x) on the interval (-1,2). Is this bound realistic?
2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given e 2.7183, e 7.3891, e 12.1825) f(1.2). a and x 2.5 to approximate f (1.5) and (b) Use cubic Lagrange interpolation based on the nodes xo=0.5, x1 =1, x2 = 2 and x, = 2.5 to approximate f(1.5) and f(12) 2019-Numerical Analysis- Quiz-2 1. Let f()-( (a) Use quadratic Lagrange interpolation based on the nodes xo 1, x 2, (given...
numerical analysis 1 f (x + 2h) f"(x) = 2f (x + h) + f (x) 12 Forward difference II f(x - 2h) f"() = 25(x - hr) 12 method Backward method difference f'(x) = -f(+ 2) + 4(x +h)- 36) 2h Forward difference method Which ones are correct? a) I, II b) Only 11 a d) Only 1 e> I, II, III
Numerical Analysis: Apply the BFGS Method to minimize the function f(x) = x12 - 2x1x2 + 4x22 with the starting point Xo = (-3,1)
I need proof of this numerical analysis theorem. This theorem is from Burden's Numerical analysis book. Please give me the detailed solution of this theorem. Theorem If {00, ... , ºn} is an orthogonal set of functions on an interval [a, b] with respect to the weight function w, then the least squares approximation to f on [a, b] with respect to w is 11 P(x) = a;°;(x), j=0 where, for each j = 0, 1, ... ,n, cb aj...
Math: Numerical Analysis 2 Let f)-In(14 ) Falyamial of arder associaled. Calculate a maximum erer evel that can ce made by estimating the value of lnC13) using the previous intbrolatim olynomial ond let P) be Mac-Lorins 2 Let f)-In(14 ) Falyamial of arder associaled. Calculate a maximum erer evel that can ce made by estimating the value of lnC13) using the previous intbrolatim olynomial ond let P) be Mac-Lorins
numerical analysis problem 4. Let s = (2,1, -4,3). Find the discrete Fourier transform F(s) of s. 5. Let w=i, s = (1, 2+2w, 3, 2-2w), t = (4,3w, 2w, -w). Find the pointwise multiplication ext.
This Question is Numerical Analysis. Please give full proof. 2. Suppose {$0(2), 01(2),..., n(x)} is an orthogonal set of functions with respect to the L2 inner product, i.e. (, = *$3 ()bu(a)dx = 0, if j tk. Prove the Pythagorean theorem ||do + + + . . ||? = ||do|l2 + ||ói || + || 6 ||º, where || | ||2 = (f, f).
Numerical analysis Question 1 The Runge's function is written as follows: f ()125x2 f (x) 1 + 25x2 a) Evaluate the given function at five equidistantly spaced values over the interval [-1,1]. (Round the b) c) d) final answers to four decimal places.) Using MATLAB, fit the obtained data with a fourth-order polynomial, and plot the result. Using MATLAB, fit the obtained data with a linear spline, and plot the result. Using MATLAB, fit the obtained data with a cubic...
Numerical Analysis hr2 h 2 f(x) = a. x3. e-(0.1)x -- +4. x. In(x) – 1500 = 0 VX + 2 We want to find the root of the above equation. (In order to ease the reading, points are used between variables. Only the number above “e” is equal to “zero point one”.) b) If "a=1.5” and “b=0.8" at the above function, find the root between Xa=50 and Xu=70 using method of false position “Regula-Falsi” until Ea of approximation satisfies...