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Problem # 1 Find the polynomial of degree 2 that interpolates at the datapoints xo = 0, Yo = 1, x1 = 1, y1 2, and r2 = 4, y2 = 2. You should get p2(t) %3D %3D 'I + + za{ - Problem # 2

Problem # 1 Find the polynomial of degree 2 that interpolates at the datapoints xo = 0, Yo = 1, x1 = 1, y1 2, and r2 = 4, y2 = 2. You should get p2(t) %3D %3D 'I + + za{ - Problem # 2

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.5: Graphs Of Functions
Problem 37E
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Problem # 5e Is the function x < 0; 0 < x< 1; -2x2 + 6x + 3, 1<r< 2; 2 < x < 3; x > 3 0, x², p(x) = (x – 3)², a spline function? Why/why not? Problem # 6e For what value of k is the following a spline function? 0 < x < 1; kæ² + (3/2), I 2x² + x + (1/2), 1<x<2. q(x) Problem # 74 Given the set of nodes xo = 0, x1 = 1/2, x2 = 1, x3 = 3/2, and x4 = 2, we construct the cubic spline function %3D 0.15B–1(x)+ 0.17Bo(x) + 0.18B1(x) +0.22B2(x)+0.30B3(x) + 0.31B4(x) +0.32B;(x), 93(x) %3D where each Bx is computed from the exemplar B spline according to (4.39). Compute q3 and its first derivative at each node. Problem # 1 e Find the polynomial of degree 2 that interpolates at the datapoints #o = 0, Yo_ = 1, ¤1 = 1, yi = 2, and x2 = 4, y2 = 2. You should get p2(t) -2 +t + 1. %3D Problem # 2 d Construct the quadratic polynomial that interpolates to y = Vr at the nodes To = 1/4, x1 = 9/16, and x2 = 1. Problem # 3 For the function below, use divided difference tables to construct the Newton interpolating polynomial for the set of nodes specified. f(x) = Va, x; = 0, 1, 4; %3D Problem # 4 Use divided difference tables to construct the separate parts of the piece- wise quadratic polynomial q2(x) that interpolates to f(x) = Vx with the nodes x = 1 2 3 4 1. 5 5 5' 5
Transcribed Image Text:Problem # 5e Is the function x < 0; 0 < x< 1; -2x2 + 6x + 3, 1<r< 2; 2 < x < 3; x > 3 0, x², p(x) = (x – 3)², a spline function? Why/why not? Problem # 6e For what value of k is the following a spline function? 0 < x < 1; kæ² + (3/2), I 2x² + x + (1/2), 1<x<2. q(x) Problem # 74 Given the set of nodes xo = 0, x1 = 1/2, x2 = 1, x3 = 3/2, and x4 = 2, we construct the cubic spline function %3D 0.15B–1(x)+ 0.17Bo(x) + 0.18B1(x) +0.22B2(x)+0.30B3(x) + 0.31B4(x) +0.32B;(x), 93(x) %3D where each Bx is computed from the exemplar B spline according to (4.39). Compute q3 and its first derivative at each node. Problem # 1 e Find the polynomial of degree 2 that interpolates at the datapoints #o = 0, Yo_ = 1, ¤1 = 1, yi = 2, and x2 = 4, y2 = 2. You should get p2(t) -2 +t + 1. %3D Problem # 2 d Construct the quadratic polynomial that interpolates to y = Vr at the nodes To = 1/4, x1 = 9/16, and x2 = 1. Problem # 3 For the function below, use divided difference tables to construct the Newton interpolating polynomial for the set of nodes specified. f(x) = Va, x; = 0, 1, 4; %3D Problem # 4 Use divided difference tables to construct the separate parts of the piece- wise quadratic polynomial q2(x) that interpolates to f(x) = Vx with the nodes x = 1 2 3 4 1. 5 5 5' 5
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