I need to do a polynomial interpolation of a set of $N$ experimental points; the functional form I have to use to interpolate is this: $$ f(x) = a + bx^2 + cx^4$$  as you can see the coefficient that I need to find are just 3: $a, b, c$; however the points I have are $N&gt;3$ and so it looks like the determination of the coefficients is impossible because over-determined. Does anyone have an idea of what should be done in such case (supposing it is even possible)?
I need to do a polynomial interpolation of a set $N$ of experimental points; the functional form I have to use to interpolate is this:  $$ f(x) = a + bx^2 + cx^4,$$ as you can see the coefficient that I need to find are just 3: $a, b, c$; however the points I have are $\#N&gt;3$ and so it looks like the determination of the coefficients is impossible because is over-determined. Does anyone have an idea of what should be done in such case (supposing it is even possible)?
Until now, I have been compiling my LaTeX documents with pdfLaTeX. My standard document preamble includes the "usual suspects" for non-English speakers (, , ) and a bunch of other packages. Assuming I were to convert to XeLaTeX, what modifications of my preamble are advisable? I'm aware that the expansion=true option of the  package is not (yet) available for XeLaTeX, and that  is sort of a default package for OpenType fonts. What other packages (and package options) should be removed and, vice versa, incorporated when switching from pdfLaTeX to XeLaTeX? Why do we need to discard one dummy variable? TikZ Angle Label - Help it "fit" better? I have the following drawn with TikZ    using the code  \documentclass{article} \usepackage{tikz} \usepackage{tkz-euclide} \usetkzobj{all} \begin{document} \begin{tikzpicture} \coordinate (O) at (0,0); \draw (O) circle (3); \coordinate[label = above left:$M$] (M) at (130:3); \coordinate[label = above:$N$] (N) at (80:3); \coordinate[label = below:$A$] (A) at (240:3); \coordinate[label =below right:$B$] (B) at (300:3); \draw (A) -- (M) -- (B); \draw (A) -- (N) -- (B); \tkzMarkAngle[draw = black, fill = white, opacity=1](A,M,B) \tkzLabelAngle[pos = 0.8](A,M,B){$x$} \tkzMarkAngle[pos = 0.2,draw = black, fill = white, opacity=1](A,N,B) \tkzLabelAngle [pos=0.8](A,N,B){$27 ^{\circ}$} \end{tikzpicture} \end{document}   Notice however, tht the 27 degrees does not fit in very nicely. How can I adapt the code to try and move the 27 a bit "lower" so that it fits in better, as well as the angle mark?  Also, how can I get two "double arrows" in the middle of lines AM and BN, to indicate that they are 'parallel'? relative polar coordinates for TikZ elements in axis environment I would like to annotate a patch plot with lines whose start and end points are given in absolute polar and relative polar coordinates, respectively.  The patch plot, based on cartesian data, comes out as a circular shape centred around the origin (0,0) and shall be simulated here by a plain circle.  Lines should start at the circumference of the shape and point away from the shape under a given angle and have a well defined length. Therefore, the use of relative polar coordinates for the line's end point.  What seems to be straightforward with TikZ (left) fails inside the axis environment of pgfplots (right): neither the inclination angle nor the length of the line are correct if relative polar coordinates are used.    What is wrong with the rel. polar coordinates here?  The code:  \documentclass{standalone}  \usepackage{pgfplots} \pgfplotsset{compat=1.13}  \begin{document}  \begin{tikzpicture}   \draw(0,0) circle[radius=0.01];   \draw[blue] (0,0) circle[radius=1];   \draw[thick] (45:1) -- ++(45:0.5); \end{tikzpicture}  \begin{tikzpicture}   \begin{axis}[tiny,enlargelimits,   axis equal,   xmin=-2,xmax=2,   ymin=-1,ymax=1,   xtick={-2,-1,0,1,2},   ytick={-2,-1,0,1,2},   grid=major,   ]   \draw[blue] (0,0) circle[radius=1];   \draw[blue, dashdotted] (0,0) -- (45:2);   \draw[thick] (45:1) -- ++(45:0.5); %  \draw[thick] (45:1) -- (45:1.5); %absolute coordinates do work   \end{axis} \end{tikzpicture}  \end{document} Can I still use the older Airport Utility 5.5.3 if I install the 6.0 version of Airport Utility? Allow diamond moderators to reverse question migrations? It has happened on occasion, due to the high amount of 10K moderators on SO that questions are migrated to the wrong site, and needs to be reversed. Although currently it is possible to re-open the question on the original site and delete the one on the destination site, it still leave the migrated too banner behind.  It would be useful if diamond moderators could reverse a migration, removing it from the destination site completely and re-activating it on the original site and at the same time removing the banners.  Previously it has been discussed educating the users around when to move questions, however this doesn't stop the problem.  As per Shog9  I have to admit I do like Shog9's suggestion regarding the post being closed as not programming related rather then re-opened, however, reasons for closing it on other sites should also be kept in mind, as this also applies to stuff being sent back forth between the sites. What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out? What prevents investors from buying high yield stocks and selling them as soon as their dividend is paid out?   I guess I am confused: If you know the yield and when the dividend will be paid out, why not buy a share an instant before the dividend is paid out and then sell it?  Do you have to have held the share for some amount of time to get the dividend? Is there too much volatility in the instant the dividend is paid out? I am moving from Malaysia to the US, and planning to bring my desktop computer with me. I plan to pack it in my checked-in luggage. Will the computer risk being damaged? Any precaution should I take to reduce this risk? Will there be any trouble with the airline or immigration about bringing computer? Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$ It is given that $X,Y \overset{\text{i.i.d.}}{\sim} N(0,1)$  Show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}} \overset{\text{i.i.d.}}{\sim} N(0,\frac{1}{4})$  I was thinking of making polar transformations $X=r \cos \theta, Y=r \sin \theta$  Then I am getting stuck at ranges of $\theta$ "Who to follow" or "whom to follow"? has a "who to follow" button on the upper side of the screen. Shouldn't it be "whom to follow"?   suggests that whom is the correct usage in a case like this. What file sizes and formats are most appropriate for enlarging and projecting an image onto a large wallspace for painting? How to get the path of a running JAR file? My code runs inside a JAR file, say foo.jar, and I need to know, in the code, in which folder the running foo.jar is.  So, if foo.jar is in C:\FOO\, I want to get that path no matter what my current working directory is. Is there a name for an element $z$ such that $\,zx = z = xz\,$ for all $x$? Is there a general name for the following properties, (similar to the properties of existence of an additive identity, existence of multiplicative identity etc):   For any given set, the intersection with the empty set results in the empty set. For any real number, multiplication with zero results in zero. Diacritics and non-English letters in anglicized loan words: keep 'em, dump 'em, italicize the words, or what? Age and Graduate school Browsing folders with more than 100000 images How do I change the default settings of export operators? I already have a 6 month valid UK business visa received prior to April 24 2015. I was supposed to travel to the UK in April, but my trip was cancelled on medical grounds.  I am now planning to visit the UK in July for tourism. Would it be fine for me to do so? Will I be allowed to enter the UK? Should I carry the original invite letter and medical certificate to prove why I didn't go the first time? Do conjugate priors just lead to a posterior that is a modification of the parameters of the prior? We know, for example, that the conjugate relationship between the classic beta-binomial is as follows:  \begin{align}  y &amp;∼ \mathcal{Bin}(n,\ θ)  \\  θ &amp;∼ \mathcal{Beta}(α,\ β)  \\ θ|y &amp;∼ \mathcal{Beta}(y + α,\  n − y + β) \end{align}  Notice how the posterior is just a change in parameterization compared to the prior. Is the posterior of conjugate priors just a change in parameters? Scaling HUD with variable resolution