Calculating Numerical Jacobian for Matrices A and B: Step-by-Step Guide

In summary, a numerical Jacobian is a tool used in numerical analysis to estimate partial derivatives of a multivariable function. It is useful for complex functions and is often used in optimization algorithms. It is calculated using finite difference methods and has limitations such as inaccuracies for functions with discontinuities or steep gradients. The accuracy can be improved by using smaller step sizes and higher-order methods. Careful selection of evaluation points is also important.
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mathia
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Hi,
I have two numerical matrices, A is 150*1 matrix (A=rand(150,1)) and B is a 1*5 matrix (B=rand(1,7)), and I need to have the jacobian of A with respect to B, that should be a 150*7 matrix, anyone help is appreciated.
Mathias
 
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Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

FAQ: Calculating Numerical Jacobian for Matrices A and B: Step-by-Step Guide

What is a numerical Jacobian?

A numerical Jacobian is a mathematical tool used in the field of numerical analysis to approximate the partial derivatives of a multivariable function. It is often used in situations where analytical methods for finding derivatives are not feasible or are too complex.

Why is a numerical Jacobian useful?

A numerical Jacobian is useful because it allows for the estimation of derivatives for complicated functions without needing to find exact analytical solutions. It is also a key component in many numerical optimization algorithms that require the computation of derivatives.

How is a numerical Jacobian calculated?

A numerical Jacobian is typically calculated using finite difference methods, which involve evaluating the function at different points and using the resulting data to approximate the partial derivatives. This process can be performed using different approaches such as forward, backward, or central differencing.

What are the limitations of a numerical Jacobian?

While a numerical Jacobian is a useful tool, it does have some limitations. For instance, it may not always provide accurate results for functions with discontinuities or steep gradients. Additionally, the accuracy of the approximation may decrease as the number of variables in the function increases.

How can the accuracy of a numerical Jacobian be improved?

The accuracy of a numerical Jacobian can be improved by using smaller step sizes in the finite difference methods and by using higher-order methods such as Richardson extrapolation. It is also important to carefully choose the points at which the function is evaluated to avoid any potential singularities or discontinuities.

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