Timeline for Algorithm for optimizing Ax = b with unknown A and known x values
Current License: CC BY-SA 3.0
17 events
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| Apr 4, 2017 at 19:35 | comment | added | Jason K. | Thanks for the clarification. So how would I describe the n value in this situation where n matches the size of the A matrix? What is the equation called if not over or under determined? | |
| Apr 4, 2017 at 19:21 | comment | added | nukeguy | The matrix size is definitely relevant. If $n$ is less than the size of $A$, then this is an underdetermined system and you can find an infinite number of $A$ matrices that yield an error of zero on your set of measurements (assuming your data does not contradict itself). If $n$ is exactly the size of $A$ (i.e., $A$ is $n \times n$), then you get exactly one $A$ which is a perfect fit. If $n$ is larger than the size of $A$, then you have an overdetermined system and some sort of least squares fitting will have to be done. Also, instead of series, you could say "system of matrix equations." | |
| Apr 4, 2017 at 5:05 | comment | added | Jason K. | I have updated the title to make it clearer and more related to the details of the question. The matrix sizes vary and did not seem relevant to the question so were not mentioned. What would be a better term than series? | |
| Apr 4, 2017 at 5:02 | history | edited | Jason K. | CC BY-SA 3.0 |
edited title
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| May 17, 2015 at 19:33 | history | tweeted | twitter.com/#!/StackSciComp/status/600021349130772482 | ||
| May 17, 2015 at 11:09 | history | edited | Christian Clason |
edited tags
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| May 11, 2015 at 19:30 | comment | added | Federico Poloni | The title and the question say two different things. It would be useful if you edited and specified clearly what is given and what is an unknown. Also, what are the matrix sizes? Are they related to $n$? And please avoid the term "series", in mathematics it means something else and it can be confusing. | |
| May 11, 2015 at 12:07 | answer | added | Bort | timeline score: 1 | |
| May 9, 2015 at 16:36 | comment | added | Jason K. | I think that ICA mentioned below is what I need. Thanks for all the suggestions. | |
| May 9, 2015 at 16:34 | vote | accept | Jason K. | ||
| May 9, 2015 at 15:26 | comment | added | Bill Barth | @Jason, if you want to formulate your problem as $Q_i R_i x_i=b_i$ so that the your $A_i$ is directly constructed from its SVD, that might be one approach instead of trying to optimize entries individually. It certainly provides some structure to your approach, but I don't think you need to be factoring your $A_i$ using QR since multiplication is massively cheaper. | |
| May 9, 2015 at 14:53 | comment | added | Jason K. | I am doing least squares as the values aren't going be exact and I am trying to derive the "best" A coefficients for a whole set of data points. I need the best fit since these are sensor readings and not the real, independent values that I would like to extract, but don't know if A has an optimum value or more than one. Bill, you are probably might be right that straight multiplication would work for this portion. My biggest problems is really getting that "best" A matrix such that I can tease out the actual values from my readings. | |
| May 9, 2015 at 13:12 | comment | added | Bill Barth | Why do you need QR to solve for $b_n$, can't you just multiply? | |
| May 9, 2015 at 10:21 | answer | added | Hari | timeline score: 9 | |
| May 9, 2015 at 9:01 | comment | added | fibonatic | How would you quantify whether $A$ has an optimum value or not? Do you have any idea what $b_n$ should look like? | |
| May 9, 2015 at 8:00 | comment | added | Geoff Oxberry | Since you're using QR, are you doing least-squares fitting? | |
| May 9, 2015 at 5:28 | history | asked | Jason K. | CC BY-SA 3.0 |