the minimum for the function below: you seek f(x, y) = Ax² - Bxy + Cy² + x - y You are given personal values for the constants A, B, and C. Also, you are given personal initial values (xo, yo) to begin your iteration.
the minimum for the function below: you seek f(x, y) = Ax² - Bxy + Cy² + x - y You are given personal values for the constants A, B, and C. Also, you are given personal initial values (xo, yo) to begin your iteration.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question
A=6 B=6 C=2 and x0=2, y0=10
![the minimum for the function below:
you seek
f(x, y) = Ax² - Bxy + Cy² + x - y
You are given personal values for the constants A, B, and C. Also, you are given personal initial
values (xo, yo) to begin your iteration.
Identify the minimum again using the Newton's method with dynamic a. However, use this
time numerical derivatives instead of Vf(x, y). When using numerical derivatives, only one
of the constants is being varied as with partial derivatives. Apply in this case the forward
numerical derivative, f'(x₁) = f(x:+h)-f(x). Here ʼn equals some very small number. For each
h
df(a)
da
= 0. When
step n, solve first the c(-1) and optimal a using the condition p'(a) =
taking the derivative of f(a), please remember to consider the inner derivatives for each of
the coordinate axes that results as dot product with the main function. In this work it is
enough that only the second term in the dot product is analyzed using numerical derivatives.
Thus, the function takes the form o'(x, y) = Vf (x − aVx, y — ay) · Vƒ (x, y).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6fab5ef8-afe0-4ae4-87da-464ac79bdd9f%2Fac1f7ac7-b23e-4342-b674-6ee699a43e91%2F73gos7a_processed.png&w=3840&q=75)
Transcribed Image Text:the minimum for the function below:
you seek
f(x, y) = Ax² - Bxy + Cy² + x - y
You are given personal values for the constants A, B, and C. Also, you are given personal initial
values (xo, yo) to begin your iteration.
Identify the minimum again using the Newton's method with dynamic a. However, use this
time numerical derivatives instead of Vf(x, y). When using numerical derivatives, only one
of the constants is being varied as with partial derivatives. Apply in this case the forward
numerical derivative, f'(x₁) = f(x:+h)-f(x). Here ʼn equals some very small number. For each
h
df(a)
da
= 0. When
step n, solve first the c(-1) and optimal a using the condition p'(a) =
taking the derivative of f(a), please remember to consider the inner derivatives for each of
the coordinate axes that results as dot product with the main function. In this work it is
enough that only the second term in the dot product is analyzed using numerical derivatives.
Thus, the function takes the form o'(x, y) = Vf (x − aVx, y — ay) · Vƒ (x, y).
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