Newton's Divided-Difference Formula To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1) distinct numbers X0, X₁,...,x, for the function f: INPUT numbers X0,X₁,...,xn; values f(xo), f(x₁),..., f(x) as Fo,0, F1,0,..., Fm,0- OUTPUT the numbers Fo,0, F1,1, ..., Fnn where i-1 Pn(x) = F0,0 + F₁(x-x₁). (Fij is flxo, X₁,.., X;].) i=1 j=0 Step 1 For i = 1, 2,...,n For j = 1,2,...,i Fij-1-Fi-1j-1 set Fij = X Xinh Step 2 OUTPUT (F0,0, F1,1,F); STOP. (Fij = f[Xi-j,...,x].)
Newton's Divided-Difference Formula To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1) distinct numbers X0, X₁,...,x, for the function f: INPUT numbers X0,X₁,...,xn; values f(xo), f(x₁),..., f(x) as Fo,0, F1,0,..., Fm,0- OUTPUT the numbers Fo,0, F1,1, ..., Fnn where i-1 Pn(x) = F0,0 + F₁(x-x₁). (Fij is flxo, X₁,.., X;].) i=1 j=0 Step 1 For i = 1, 2,...,n For j = 1,2,...,i Fij-1-Fi-1j-1 set Fij = X Xinh Step 2 OUTPUT (F0,0, F1,1,F); STOP. (Fij = f[Xi-j,...,x].)
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
Related questions
Question
Make an actual code equivalent in MATLAB. Include the table showing the parameter values for each interpolate. Include graphs.
![Newton's Divided-Difference
Formula
To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1)
distinct numbers X0, X₁,...,x, for the function f:
INPUT numbers X0,X₁,...,xn; values f(xo), f(x₁),..., f(x) as Fo,0, F1,0,.., F,0-
OUTPUT the numbers Fo,0, F1,1, ..., Fnn where
i-1
Pn(x) =F0,0 +Fij(x-x₁). (Fij is flxo,X₁,..., X;].)
j=0
Step 1 For i = 1,2,...,n
For j = 1,2,...,i
set Fij
Fij-1-Fi-1j-1
X Xinh
Step 2 OUTPUT (F0,0, F1,1,F);
STOP.
i=1
=
(Fij = f[Xi-j,...,x;].)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2086347b-27d5-4b23-a6f3-2066a456f282%2Fb79ce4d7-82b7-4b1e-9c9a-95190c089fc2%2Fd2v75x_processed.png&w=3840&q=75)
Transcribed Image Text:Newton's Divided-Difference
Formula
To obtain the divided-difference coefficients of the interpolatory polynomial P on the (n+1)
distinct numbers X0, X₁,...,x, for the function f:
INPUT numbers X0,X₁,...,xn; values f(xo), f(x₁),..., f(x) as Fo,0, F1,0,.., F,0-
OUTPUT the numbers Fo,0, F1,1, ..., Fnn where
i-1
Pn(x) =F0,0 +Fij(x-x₁). (Fij is flxo,X₁,..., X;].)
j=0
Step 1 For i = 1,2,...,n
For j = 1,2,...,i
set Fij
Fij-1-Fi-1j-1
X Xinh
Step 2 OUTPUT (F0,0, F1,1,F);
STOP.
i=1
=
(Fij = f[Xi-j,...,x;].)
Transcribed Image Text:Hermite Interpolation
To obtain the coefficients of the Hermite interpolating polynomial H(x) on the (n + 1)
distinct numbers xo,...,x for the function f:
INPUT numbers xo, X₁,...,x; values f(xo),..., f(x) and f'(xo),..., f'(x₂).
OUTPUT the numbers Q0.0, Q1,1... Q2n+1,2n+1 where
H(x) =
Q0,0 +₁,1(x-xo) + Q₂₂(x − xo)² + Q3,3(x − xo)²(x − x₁)
+Q4.4(x-xo)²(x − x₁)²+...
+Q2n+1,2n+1(x-xo)²(x − x₁)²(x − xn−1)²(x − xn).
Step 1 For i = 0, 1,...,n do Steps 2 and 3.
Step 2 Set Z2 = Xis
Z2i+1=X₁;
Q21,0 = f(x₁);
Q2i+1,0 = f(x₁);
Q2i+1,1 = f'(x₂).
Step 3 If i #0 then set
Q2,1 =
Step 4 For i = 2, 3,..., 2n + 1
Q21,0-2-1,0
Z2i-Z2-1
=
for j = 2, 3,..., i set Qi.j :
Qi.j-1-Qi-1.j-1
Zi-Zi-j
Step 5 OUTPUT (Q0.0, Q1,1,Q2n+1,2n+1);
STOP
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 4 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, computer-science and related others by exploring similar questions and additional content below.Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education