@pyr666 Richardson extrapolation goes only one level down. Romberg will take values from Richardson's extrapolation and get a better answer. Then it will use those to get better answers and so on.
@Soumilbharatendu A1, A2, A3 are the approximate constants of proportionality. If true error is approximately proportional to h^2, then we can assume true error approximately = A1*h^2. For more details, go to numericalmethods(dot)eng(dot)usf(dot)edu, click on Keyword, click on Romberg, and read the textbook chapter. To get even more basic, click on Trapezoidal rule, read the error section of the textbook chapter and the video on the error section.
Soon, we will be annonating these new videos to link to the videos that show the formula derivation. Meanwhile, go to the playlist called Romberg at the numericalmethodsguy channel and you will see the derivation of the first order approximation.
@Soumilbharatendu This is a course for scientists and engineers. I do not have specific course for EEs. You can look at the numericalmethods(dot)eng(dot)usf(dot)edu which has applications in EE of numerical methods.
I have knowledge around calclus 1 and some calculus 2 knowledge. I've never heard of Romberg Integration until messing about with the Mac Grapher software. What do I need to know this for, where is it useful? What pre-requisites do I need to know for tackling this topic?
In addition to Calculus 2, you just need to understand Numerical Integration - mathforcollege.com/nm/mws/gen/07int/index.html and estimates of true errors in numerical integration. It is useful for fast integration of functions. You can achieve the numerical integration by just the trapezoidal rule but the efficiency of the Romberg integration can throw the trapezoidal rule in the dust!
awesome site, thanks for your answer. I like that clear pre-requisites and objectives are outlined. The content seems to be structured in a good order of complexity. I will definitely spend some time on this material.
Numerical methods such as Romberg integration are useful in computer modeling. You can take data and then use techniques like Romberg integration to approximate what is happening between the data points, eventually deriving a model (still just an estimation) of how, say, a plume of smoke rises out of a stack or how wastewater will disperse when dumped into a river.
God bless you professor, I'm an electrical engineer and for the love of me my mathematics teacher makes this too deep.
This is a lot better than how my teacher puts it.
Nicely explained sir
Thank you very much.
@pyr666 Richardson extrapolation goes only one level down. Romberg will take values from Richardson's extrapolation and get a better answer. Then it will use those to get better answers and so on.
Fantastic video! Thanks!
Great explanation, thank you
@Soumilbharatendu A1, A2, A3 are the approximate constants of proportionality. If true error is approximately proportional to h^2, then we can assume true error approximately = A1*h^2. For more details, go to numericalmethods(dot)eng(dot)usf(dot)edu, click on Keyword, click on Romberg, and read the textbook chapter. To get even more basic, click on Trapezoidal rule, read the error section of the textbook chapter and the video on the error section.
Soon, we will be annonating these new videos to link to the videos that show the formula derivation. Meanwhile, go to the playlist called Romberg at the numericalmethodsguy channel and you will see the derivation of the first order approximation.
Great video.
Very nice,Thank you very much sir. Sir, could you just explain me one thing that what are A1,A2,A3,... I didn't understand that part very much
This is just a description of the formulas, i think that explaining how these formulas are deducted would be more important...
Exactly. I did not understand the derivation of the formulae, nor the meaning of them((
you have to say that the 3 is came from 2´2-1 and the 15 cames from 4´2-1
excatly...instead he messed up saying 15 came from h^4.....its richardson extrapolaion formulae that gives 4^(i-1) ---1
Superb! Thank you!
@Soumilbharatendu This is a course for scientists and engineers. I do not have specific course for EEs. You can look at the numericalmethods(dot)eng(dot)usf(dot)edu which has applications in EE of numerical methods.
Thnk u sir...much information given with in less time
sir;
i just wanted to ask that do we have this course of numerical analysis(problem soving through computer)in electrical engineering or not.
I have knowledge around calclus 1 and some calculus 2 knowledge. I've never heard of Romberg Integration until messing about with the Mac Grapher software. What do I need to know this for, where is it useful? What pre-requisites do I need to know for tackling this topic?
In addition to Calculus 2, you just need to understand Numerical Integration - mathforcollege.com/nm/mws/gen/07int/index.html and estimates of true errors in numerical integration. It is useful for fast integration of functions. You can achieve the numerical integration by just the trapezoidal rule but the efficiency of the Romberg integration can throw the trapezoidal rule in the dust!
awesome site, thanks for your answer. I like that clear pre-requisites and objectives are outlined. The content seems to be structured in a good order of complexity. I will definitely spend some time on this material.
Numerical methods such as Romberg integration are useful in computer modeling. You can take data and then use techniques like Romberg integration to approximate what is happening between the data points, eventually deriving a model (still just an estimation) of how, say, a plume of smoke rises out of a stack or how wastewater will disperse when dumped into a river.