I will confine my question to the simple case of constructing a linear fit of one independent variable $X$ and one dependent variable $Y$, with no intercept term.  The sample predictions are $\hat y_i = \beta x_i$. Define the $p$-norm as  $$L^p = \left(\sum_{i=1}^n \vert y_i - \hat y_i \vert^p \right)^\frac{1}{p}$$  And define the $L^p$-regression of a sample $\lbrace x_i, y_i\rbrace_{i=1}^n$  as  $\beta$ such that $L^p$ is minimized.  I know how to do a least-squares ($L^2$) regression by solving the normal equations. I have also seen a linear programming procedure that does $L^1$ regression (minimizes the mean absolute error). And in the general case, you can define a reasonable search space and use numeric methods to find $\beta$ for arbitrary $p$.   I am wondering about the $p=\infty$ case. It can be shown that   $$L^\infty = \max \lbrace \vert y_i - \hat y_i \vert \rbrace$$  so an $L^\infty$ regression would amount to finding the value of $\beta$ that minimizes the maximum error.  Can this be solved explicitly, or do I need to use numeric methods?
Is there any software package to solve the linear regression with the objective of minimizing the L-infinity norm.
Scoping in assigning a derivative Linear independence of $\sin(x)$ and $\cos(x)$ In the vector space of $f:\mathbb R \to \mathbb R$, how do I prove that functions $\sin(x)$ and $\cos(x)$ are linearly independent. By def., two elements of a vector space are linearly independent if $0 = a\cos(x) + b\sin(x)$ implies that $a=b=0$, but how can I formalize that? Giving $x$ different values? Thanks in advance. Killing form on $\mathfrak{sp}(2n)$ Can I change the color of the last selected face? I am playing with LINQ to learn about it, but I can't figure out how to use Distinct when I do not have a simple list (a simple list of integers is pretty easy to do, this is not the question). What I if want to use  on a list of an Object on one or more properties of the object?  Example: If an object is Person, with Property Id. How can I get all Person and use Distinct on them with the property Id of the object?  Person1: Id=1, Name="Test1" Person2: Id=1, Name="Test1" Person3: Id=2, Name="Test2"   How can I get just Person1 and Person3? Is that possible?  If it's not possible with LINQ, what would be the best way to have a list of Person depending on some of its properties in .NET 3.5? Does this recording sound like the pulses emitted by bats? Out of curiosity, I recorded sounds in an area with lots of bats, hoping to be able to &quot;hear&quot; the bats communicating by lowering the ultrasound to a level down to the frequency which can be heard by a human. After a bit of post-processing, I actually hear interesting sounds, but I'm not sure about the origin. It seems that the frequency of the pulses is too low compared to bats. . Are those actual sounds emitted by bats? If not, what other animal could be the source of those sounds? About the audio The sound was recorded at 10 p.m. at  near a river, with more of a dozen bats flying in this zone. There is a bridge nearby, and the sides of the river are flat concrete, which means that there are a lot of opportunity for sound reflection (although high frequency sounds don't reflect well). Zoom H5 with the default XY directional microphone was used. The bitrate was set to 24-bit. Unfortunately, I used the sampling frequency of 48 kHz instead of the maximum 96 kHz. The following transformations were made to the original audio:  The pitch was shifted by -12 semi-tones, which means that the 20 kHz sound becomes 10 kHz, and 15 kHz becomes 7.5 kHz.   All sounds below 6 kHz were removed.  The sound was amplified.  Severe noise reduction was applied to eliminate everything but the actual sounds emitted by the bats.   The empty parts of the audio were removed.  The sound was amplified once again.   Frequency The frequency analysis of the transformed audio a peak around 9 kHz (18 kHz in the original audio), slowly fading to suddenly drop at 16 kHz (32 kHz in the original audio).   contains many sources with different indications about the frequency range of the sounds emitted by bats, only a few referencing the frequencies low enough to be heard by a human:  Frequency Produced 10kHz-120kHz Ramsey, Gabriel, McGuirk, Phillips, Watenpaugh. Holt Physical Science. New York: Holt, Rinehart and Winston Publishers, 1986.  while most agreeing on the fact that bats use frequencies higher than 20 kHz.  Most bats use frequencies in the range 20-80 kHz, only a few bats use frequencies less than 20 kHz. Long, M.R. &amp; Savage, J.G. Mammal Evolution. New York: Harper, 1976: 108.  The observed range of 18..32 kHz seems too low compared to the sources, but I have an impression that the frequencies vary a lot between different species of bats. Pattern When viewing the audio track (see below), each cry consists of several pulses in two to three sub-groups which are in turn in two groups. Each peak is a bit less than 1 ms. The second group occurs from 40 to 200 ms. after the end of the first one. Each sub-group is separated by 5 to 10 ms. The frequency of every pulse doesn't vary, except the very first pulse. The first cry starts by a more quiet pulse at 6 kHz (12 kHz in the original audio). The second and third cries don't follow this pattern.  indicates that there are three categories of sounds emitted by the bats:  Short clicks,  Frequency-swept pulses,  Constant frequency pulses.   It looks like it's still the third category which we are observing here, and the overall pattern looks similar to the one described for the bats. The gap between the left and the right track is mostly irrelevant: at higher frequencies, microphones become more and more directional, and the sound is reflected less, which leads to such difference.     Note: this question was considered to be on-topic at Biology.SE on . When I capture packets using the packet analyser wireshark while visiting  I can see packets that use the HTTP protocol (e.g.a GET request). My Get request uses 4 protocols: Ethernet II, IPv4, TCP and HTTP.  For the IPv4 I can see my own local IPv4 address of my pc as the source, for the destination I see the IPv4 address 91.198.174.225. When I go to this address in my browser I get to some wikipedia related website that says'wiki does not exist'. Why am I not seeing the Hydrogen article when I go to that ip address? is there any extra latency using an amp sim on wine? I want to use AmpliTube amp sim on ubuntu studio but there isn't a linux version for it, can I just use wine and will it have any extra latency? if so how much latency? “community wiki” checkbox in new question shows a dialog twice when self-answering Click Answer your own question Check community wiki A dialog box     Are you sure you want to make this post Community Wiki?   will appear, Click OK or Cancel; The same dialog will appear again.   Google Chrome 44.0.2403.107 / Windows8.1 / site rev 2015.7.25.3609 I am often logged in several SSH sessions at once. To logout from several sessions, I press CTRL+d, until I am back on my local machine. However, I occasionally press it once too many, and my terminal exits. Is there a way to make CTRL+d unable to close my terminal ? I am using terminator as my terminal emulator. How to make sense out of the $\epsilon-\delta$ definition of a limit? The informal intuition for the limit of a function is this:     What is the value of the function $f$ as $x$ gets infinitely close to $c$?   How on earth does this monster  $$ \lim_{x \to c} f(x) = L  \iff  (\forall \varepsilon &gt; 0)(\exists \ \delta &gt; 0) (\forall x \in D)(0 &lt; |x - c | &lt; \delta \ \Rightarrow \ |f(x) - L| &lt; \varepsilon)$$ capture our intuition?  I want the answer to explain and motivate every bit of this formal statement. Remember: I am able to parse the statement, I just don't see how it captures our informal intuition. Can airlines deny boarding if my port of entry is different than the country which issued the Schengen visa? Few days back I did a Europe tour from India. As stated by many (I haven't confirmed official documents), I can apply for a visa from the country which is either my first port of entry in this case Paris or the longest stay which in this case was Italy.  Now following is what happened with me.   My flight was New Delhi to Paris via Istanbul with Turkish Airlines I Traveled from New Delhi to Istanbul (no problem here). When I was boarding to flight Istanbul to Paris, zhe airlines officials (the ones who checks the boarding pass before boarding the flight) told me that I could not board the flight because my visa was issued by Italy and I need to go to Italy First. They were denying the longest stay option of the visa. Moreover NONE of the staff of Istanbul airport were able to understand English so I had to go to a lot of problems before I managed to get tickets to Venice. I somehow managed to fly to Venice from Istanbul after almost 24 hours of struggle at Istanbul airport (without food and water).   So, my question is do the airlines staff have a right to deny flight boarding in this case? `du -sh` reports different used size than `df -h` Possible Duplicates:             df -h says that I have 494G used on /var:  Filesystem            Size  Used Avail Use% Mounted on /dev/sda3             564G  494G   41G  93% /var   But du -sh /var says it's 350G  What makes them different? Best way to strike out a text Why does Ubuntu keep asking for my gmail password? How can I run ssh-add automatically, without a password prompt? I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine?  I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine.  if [ -z "$SSH_AUTH_SOCK" ] ; then     eval `ssh-agent -s`     ssh-add fi I know I use them, and my peers use them, but how much does the average user actually use tooltips to figure out functionality? Tensor product vs. Cartesian Product for composite quantum systems What is the reason the log transformation is used with right-skewed distributions? I once heard that      log transformation is the most popular one for right-skewed distributions in linear regression or quantile regression   I would like to know is there any reason underlying this statement? Why is the log transformation suitable for a right-skewed distribution?   How about a left-skewed distribution? How to know the motherboard BIOS version using the command line How can get the BIOS version of my motherboard?  The command dmidecode gives you some information about the BIOS, but I can't find what I need...    I tried dmidecode command before asking and I didn't find what I needed - I want only the BIOS version and nothing else in the output.