Problem # 5e Is the function 0, x2, -2x² + 6x + 3, 1< ¢< 2; (x – 3)², 0, x < 0; 0 3 a spline function? Why/why not?
Problem # 5e Is the function 0, x2, -2x² + 6x + 3, 1< ¢< 2; (x – 3)², 0, x < 0; 0 3 a spline function? Why/why not?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
solve problem 5 with explanation asap
![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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0040300a-f1d3-4d0b-9bcd-76ec4868bdb4%2F239263a6-1f4e-41a6-bf17-38adf470dfd0%2F0af124q_processed.jpeg&w=3840&q=75)
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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