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Numerical Analysis and Simulation
The study of algorithms for problems related to continuous mathematics
818 Questions
How do you calculate the frequency?
Count the number of events occurring during a time period. Then frequency = number of events/length of time period.
The concept of the Everett's formula for interpolation?
Unfortunately I can't find any freely available information about the concept/theory/derivation of the Everett formula, I can find the equation fine but none of the theory related to it, and it's not covered in any of my text books that go well beyond my university course where I have also taken all available numerical analysis modules.
All I can say is that to me this seems like quite an advanced theory, and if you're in university/college, your best bet is to ask your lecturer/teacher about the theory behind it if you don't understand it properly. If you're not at university, then I'm sorry that I can't be of any use to you, but as I stated in the first paragraph, this is not covered in any of my courses, or any of my textbooks, and I have tried looking for the necessary information elsewhere but I can't find it.
What does the word manipulated variable mean?
A manipulated variable is essentially the same as an independent variable in the context of scientific research.
Here's an example. Suppose you were studying how quickly rats can navigate a maze to find food and you wanted to know the effect of hunger level. You could keep one group of rats hungry for four hours and another group hungry for eight hours then allow each rat in the two groups to find its way through the same maze to a quantity of food. You would measure the time it took each rat to find the food. The manipulated variable would be the time that a rat had been kept hungry.
Fixed point iteration methods plus algorithm?
There are 2 main methods for fixed point iteration, the Newton-Raphson method, and the Secant method.
This method uses the formula, xn+1 = xn - f(xn) / f'(xn),
where xn is the initial point, f(xn) is the value of the function at that point, and f'(xn) is the value of the differentiated function at that point. Plug all these values into the above equation to get xn+1, which then becomes the next initial point. Repeat until you get a point within an acceptable degree of error.
the formula for this method is, xn+1= xn - (f(xn)(xn - xn-1)) / (f(xn) - f(xn-1)).
With this formula you do not need the differentiated form of the function, making this a better method than the N-R for functions difficult to differentiate. However you do need two initial points for this method to work (xn and xn-1). Again just plug the appropriate values into the formula to generate the next point approximation.
NB: with both of these methods be careful which initial point you choose, especially with the N-R method, as depending on the function the approximation iterations can go out of control and zoom away from the point you're trying to find.
Also, a note on errors, you can sometimes get a better approximation by fiddling with your function a bit and reducing the amount of calculations needed. For example if you have two equivalent functions, but one takes 3 calculations to get a value and the other takes 6, the latter takes more work and will generally give a bigger error than the previous. Usually this error increase is only marginal, but depending on the function and the values used, the potential error can be huge. This only needs to be taken into account though if you want extremely accurate results. (Things to look out for if trying to reduce error: subtracting near equal numbers, dividing by a small number or multiplying by a large number, cancellation of significant figures)
What does it mean to make a conjuncture?
Conjuncture is basically a joining of objects words or phrases. So to make a conjuncture would be to join things together. In propositional calculus making a conjuncture would mean joining a string of statements together.
Example: given the two statements
IF All A's are letters;
And All letters are are in the alphabet;
then the Conjuncture would be
All A's are in the alphabet.
Is 5 pounds of sugar bigger than 75 oz of chocolate?
5 x 16 = 80 oz sugar
so 5lb has more mass than 75 oz
What are the linear and nonlinear image enhancement methods?
Linear image enhancement methods involve operations that apply a linear transformation to pixel values, such as histogram equalization, contrast stretching, or filtering with linear kernels. These techniques preserve the relationships between pixel intensities, making them suitable for improving overall image quality. Nonlinear image enhancement methods, on the other hand, utilize transformations that do not maintain linearity, such as gamma correction, adaptive histogram equalization, or morphological operations. These methods are often used to enhance specific features or details in an image that linear methods may overlook.
What is the order of Runge-Kutta method in a modified Euler's method?
Typical application of Runge-Kutta is a fourth order method. See related link.
What are the advantages of the Euler's modified method over Euler's method?
The advantage of the modified method is the improved accuracy - the error is of order h3 as opposed to h2, where h is the step size. Since the step size is required to be small for the methods to give fair approximations (h<<1), the error is less on the modified method.
What are the opportunities and shortcomings of the quantitative approach?
The quantitative approach offers the opportunity for precise measurement and statistical analysis, enabling researchers to identify patterns and relationships within data. It allows for large sample sizes, enhancing the generalizability of findings. However, its shortcomings include a potential neglect of context and depth, leading to an oversimplification of complex phenomena. Additionally, reliance on numerical data can overlook subjective experiences and qualitative insights that are crucial for a comprehensive understanding.
What is the Real root of 1-0.6x divided by x using bisection method?
The root of f(x)=(1-0.6x)/x is 1.6666...
To see how the bisection method is used please see the related question below (link).
it means how much the current asset is worth in the market
What is the derivative of y equals aex plus be2x plus ce3x with respect to x?
if y=aex+be2x+ce3x then its derivative dy/dx or y' is:
y'=aex+2be2x+3ce3x
