demonstrate the use of the method with reflections on the use of numerical methods, as described below. As your main task, you seek the minimum for the function below:f(x,y)=Ax^2-Bxy+Cy^2+x-yA= 2 B= -2 C= 1 X0= 4 y0=41.Identify the minimum for the function using the vectoral application of Newton's method while applying dynamic . Thus, you need to optimize for each iteration step to improve performance and avoid overshoot. Use iterations to find the solution with the accuracy of five significant numbers. 2.Identify the minimum again using the Newton's method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step, solve first the and optimal using the condition. When taking the derivative of, 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 .
demonstrate the use of the method with reflections on the use of numerical methods, as described below. As your main task, you seek the minimum for the function below:f(x,y)=Ax^2-Bxy+Cy^2+x-yA= 2 B= -2 C= 1 X0= 4 y0=41.Identify the minimum for the function using the vectoral application of Newton's method while applying dynamic . Thus, you need to optimize for each iteration step to improve performance and avoid overshoot. Use iterations to find the solution with the accuracy of five significant numbers. 2.Identify the minimum again using the Newton's method with dynamic . However, use this time numerical derivatives instead of . When using numerical derivatives, only one of the constants is being varied as with partial derivatives. Apply in this case the forward numerical derivative, . Here equals some very small number. For each step, solve first the and optimal using the condition. When taking the derivative of, 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 .
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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Transcribed Image Text:demonstrate the use of the method with reflections on the use of
numerical methods, as described below. As your main task, you seek
the minimum for the function below:f(x,y)=Ax^2-Bxy+Cy^2+x-yA= 2 B=
-2 C= 1 X0= 4 y0=41.Identify the minimum for the function using the
vectoral application of Newton's method while applying dynamic . Thus,
you need to optimize for each iteration step to improve performance and
avoid overshoot. Use iterations to find the solution with the accuracy of
five significant numbers.
2.Identify the minimum again using the Newton's
method with dynamic . However, use this time numerical derivatives
instead of. When using numerical derivatives, only one of the constants
is being varied as with partial derivatives. Apply in this case the forward
numerical derivative, . Here equals some very small number. For each
step, solve first the and optimal using the condition. When taking the
derivative of, 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 .
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