I have been doing some research lately about numerical analysis textbooks, but I have not found anything successfully. I was wondering if there is like some sort of standard, for example, whenever someone mentions Calculus, I would think of Spivak or Stewart. I do not have any background nor experience on the subject, so readability counts, and I am a first year undergraduate student. Hopefully I made my point.
I'm in a numerical analysis course right now and it's pretty rigorous but I'm enjoying it a lot. I took a lower level course before that was more oriented towards implementation of numerical methods, so it's not my first time with the material.  Anyway, my professor wrote his own course notes and they're fantastic but I wanted some reference material since I'm currently outlining my own notes. Just wondering what the big ones out there are  edit: I would say I'm at an advanced undergraduate level
What is the most effective way for float and double comparison? Use SUM In Update Statement I am attempting to use SUM() in my SET statement for my UPDATE.  When I try this, I get an error of      Msg 157, Level 15, State 1, Line 234   An aggregate may not appear in the set list of an UPDATE statement.   What should I alter in my CTE so that I can run this update?    ;WITH CTE AS  (Select EC, CN, CID, EntryDate         FROM OPENQUERY(192.55.108.214,'select                                count(es.estimatenumber) As EC                               ,cm.an CN                               ,cm.am CID                               ,es.entrydate EntryDate                               from etalac es                                INNER JOIN bacalac cm                               ON es.CID = cm.am                               GROUP BY cm.an, cm.am, es.entrydate')) UPDATE d2016 SET TotalNumber = SUM(EC) FROM CTE cte INNER JOIN datafor16 d2016 ON cte.CID = ed2016.CID WHERE CAST(entrydate As Date) BETWEEN '01/01/2016' AND '01/22/2016'; What does "href" stand for in HTML? Extreme learning machine: what's it all about? I've been thinking about, implementing and using the Extreme Learning Machine (ELM) paradigm for more than a year now, and the longer I do, the more I doubt that it is really a good thing. My opinion, however, seems to be in contrast with scientific community where -- when using citations and new publications as a measure -- it seems to be a hot topic.  The ELM has been introduced by  around 2003. The underlying idea is rather simple: start with a 2-layer artificial neural network and randomly assign the coefficients in the first layer. This, one transforms the non-linear optimization problem which is usually handled via backpropagation into a simple linear regression problem. More detailed, for $\mathbf x \in \mathbb R^D$, the model is  $$ f(\mathbf x) = \sum_{i=1}^{N_\text{hidden}} w_i  \, \sigma\left(v_{i0} + \sum_{k=1}^{D} v_{ik} x_k \right)\,.$$  Now, only the $w_i$ are adjusted (in order to minimize squared-error-loss), whereas the $v_{ik}$'s are all chosen randomly. As a compensation for the loss in degrees-of-freedom, the usual suggestion is to use a rather large number of hidden nodes (i.e. free parameters $w_i$).  From another perspective (not the one usually promoted in the literature, which comes from the neural network side), the whole procedure is simply linear regression, but one where you choose your basis functions $\phi$ randomly, for example  $$ \phi_i(\mathbf x) = \sigma\left(v_{i0} + \sum_{k=1}^{D} v_{ik} x_k \right)\,.$$  (Many other choices beside the sigmoid are possible for the random functions. For instance, the same principle has also been applied using radial basis functions.)  From this viewpoint, the whole method becomes almost too simplistic, and this is also the point where I start to doubt that the method is really a good one (... whereas its scientific marketing certainly is). So, here are my questions:   The idea to raster the input space using random basis functions is, in my opinion, good for low dimensions. In high dimensions, I think it is just not possible to find a good choice using random selection with a reasonable number of basisfunctions. Therefore, does the ELM degrade in high-dimensions (due to the curse of dimensionality)? Do you know of experimental results supporting/contradicting this opinion? In the linked paper there is only one 27-dimensional regression data set (PYRIM) where the method performs similar to SVMs (whereas I would rather like to see a comparison to a backpropagation ANN) More generally, I would like to here your comments about the ELM method. Tempdb Add files require Restart Does adding Tempdb files require a restart? We would like to Add files on the same drive, Not Delete and Not modify. We tested in Dev and QA environment, restart was not required. However for production I would like to be sure everything works properly. Some are stating conditions, not always necessary, sometimes necessary, I am reading resources below:  ALTER DATABASE [tempdb] ADD FILE ( NAME = N'tempdev2', FILENAME = N'G:\tempdb2.ndf' , SIZE = 12288000KB , MAXSIZE = UNLIMITED, FILEGROWTH = 0 ) GO ALTER DATABASE [tempdb] ADD FILE ( NAME = N'tempdev3', FILENAME = N'G:\tempdb3.ndf' , SIZE = 12288000KB , MAXSIZE = UNLIMITED, FILEGROWTH = 0    Do You Need an Outage to Add tempdb files? Brent Ozar  "Technically, not always. But practically speaking, yes. If you have to shrink files, that’s very difficult while SQL Server is in use, and we’ve seen cases where anti-virus/file control tools didn’t act up until SQL Server was restarted after the files were added."   "Once the additional files have been created, it’s not always necessary to perform a service restart.  However, in many production environments, simply modifying the filesize of the existing TempDB datafile (tempdev) is not possible without restarting services first. "  The following resources are saying no restart required: How do I add a Pokestop to an area that has none? It is an area where there are tons of businesses but unless I drive about a mile from my work area there are no Pokestops.   I want to add one since we have 1000's of people in the work area, a lot of them play Pokemon Go, and we all can't leave work to drive a mile away to get to a Pokestop area.   Plus it would be nice to be able to capture Pokemon on our breaks. My friend recently received a new digital drawing tablet (Wacom Intuos Pro). Among other features, there is a hole that resembles a charm hole found on mobile phones:    Other parts of the package (e.g. pen) do not have such holes, so it isn't possible to attach them using a band. What is the purpose of this hole? Is it just for attaching various charms and such? How to convert a HEIF/HEIC image to JPEG in El Capitan? So, here’s the thing. I have a new iPhone and an old Mac. iOS 11 (still in beta as of today) and El Capitan (no more updates for this Mac). I use iCloud photo library in both devices. When I take a photo in the new format with my iPhone 7, is there any way to use it right away in my mac, without having to convert it in my iPhone first? I mean, can I get those photos synced through iCloud and converted locally on my Mac?  I have tried to find a third party software that could do that kind of conversion, but was not able to find any that would work on El Capitan. Any idea? This question is pretty simple: I'd like to have the possibility to get the exact size of a picture in LaTeX with, for example, the macro \the.  In fact, I've founded the way \settoheight{} and so on, but it didn't work at all. What I've got doesn't match with what I can see in the image properties (I suppose that's the name in English). The result: 8pt versus 1300 pixels. It's may be a mis-use...  Edit: In the end, my aim was to find a way to fit the picture in LaTeX. If width and height were both less than the dimensions of the body, then it should just be centred. It look like this :     Require:   \usepackage{graphicx} \usepackage{xifthen} \usepackage{calc}   Code (pretty ugly, I agree):   % Centrering+fitting for image, with captation and label (not auto) \newlength\imageheight \newlength\imagewidth \newcommand{\pic}[3]{% \settoheight\imageheight{\includegraphics{pictures/#1.png}}% \settowidth\imagewidth{\includegraphics{pictures/#1.png}}% \ifthenelse{\lengthtest{\imagewidth &gt; \textwidth}}{\ifthenelse{\lengthtest{\imageheight &gt; \imagewidth}}{\par\vspace{0.95em}% \begin{figure}     \centering\includegraphics[height=0.85\textheight]{pictures/#1.png}     \caption{#2}     \label{#3} \end{figure}% \par\vspace{0.95em}}{\par\vspace{0.95em}% \begin{figure}     \centering\includegraphics[width=0.95\textwidth]{pictures/#1.png}     \caption{#2}     \label{#3} \end{figure}% \par\vspace{0.95em}}}{\ifthenelse{\lengthtest{\imageheight &gt; \textheight}}{\par\vspace{0.95em}% \begin{figure}     \centering\includegraphics[height=0.85\textheight]{pictures/#1.png}     \caption{#2}     \label{#3} \end{figure}% \par\vspace{0.95em}}{\par\vspace{0.95em}% \begin{figure}     \centering\includegraphics{pictures/#1.png}     \caption{#2}     \label{#3} \end{figure}% \par\vspace{0.95em}}}} %   To use it : put your png files in a "pictures" directory, then, just simply call the picture like this : \pic{name_whitout_extension}{Captation_if_needed}{Label_if_needed}.    Edit 2 :   Thanks to Martin Scharrer's easyfig package, I've got a more or less 1,6 times faster solution to put my pictures, centred, with the perfect size.  CTAN:   VC:   Version v1.2 – 2012/05/15    This could be useful for some others, I hope. Is the below brief explanation correct and complete (at least in context)? Can it be improved/simplified without getting technical? I am especially concerned about the last sentence: Is that reasoning absolutely clear to a layman?            The problem can be viewed as drawing the above graph without lifting your hand and without retracing a line. Observe that each dot is connected by three lines. Also observe that you have to draw a line to arrive at a dot, and you have to draw a line to leave that dot. Because each dot is connected by three lines, each must be visited twice. But it is impossible to visit each dot twice (even number of times) and end up with each dot connected with three lines (odd number of times). I am trying to construct a theoretical Diffie-Hellman key exchange protocol. However, i cannot understand the difference between choosing an additive group or a multiplicative group. I believe an additive would make it much more simple, but would a multiplicative group make it more difficult to break? What would be the difference between the use of those 2 kinds of number groups? Can HTML5 databases and localStorage be shared across subdomains? I was given this problem 30 years ago by a coworker, posted it 15 years ago to rec.puzzles, and got a solution from Barry Wolk, but have never seen it again.  Consider the series:  $$1, \frac{1}{2},\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}},\frac{\displaystyle\frac{\displaystyle\frac{1}{2}}{\displaystyle\frac{3}{4}}}{\displaystyle\frac{\displaystyle\frac{5}{6}}{\displaystyle\frac{7}{8}}},\cdots$$  Each fraction keeps its large bars while being put atop a similar structure. This can also be represented as $$\frac{1\cdot 4 \cdot 6 \cdot 7 \cdot\cdots}{2 \cdot 3 \cdot 5 \cdot 8 \cdot\cdots}$$ terminating at $2^n$ for some $n$, where it is much closer to the limit than elsewhere.  The challenge:   Find the limit, not too hard by experiment In the last expression, find a simple, nonrecursive, expression to say whether $n$ is in the numerator or denominator Prove the limit is correct-this is the hard one. My directory (in Linux) looks like com/com/{various,files} where com and com are folders of the same name and the second com holds the various files. I want the first com removed, but the second and files in the second kept. How do I find this limit: $\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right]$? I'm working on a practice exam for my masters quals and I am having difficulties with the following limit. According to wolfram alpha, it's value is 1/2. Does anyone know how to find this limit?   $$\lim_{n\to\infty} \left[ n-{n\over e}\left(1+{1\over n}\right)^n \right].$$ I’m reading Shakespeare’s Henry IV (Part 1) right now and I’m noticing that Sir John Falstaff has a propensity of saying “If this, then I’m a this” sort of statements. A few examples to clarify:     … An I   have not ballads made on you all and sung to filthy   tunes, let a cup of sack be my poison      An I have not   forgotten what the inside of a church is made of, I   am a peppercorn, a brewer’s horse      if manhood, good manhood, be   not forgot upon the face of the earth, then am I a shotten herring      If I do not beat thee out of thy   kingdom with a dagger of lath, and drive all thy   subjects afore thee like a flock of wild-geese,   I’ll never wear hair on my face more   Is there a particular literary term for these sort of sentences? A composition of a periodic function that is somehow not periodic. How can I set up password-less SSH login? Calculating half derivative of $x$ using Cauchy's repeated integral formula As far as I know, Cauchy's repeated integral formula is defined as: $$(I^nf)(t)=\frac{1}{\Gamma(n)}\int_a^x (x-t)^{n-1}\space f(t)\space\space dt,\space\space n\notin Z_{\le 0}$$  I know that Gamma function is not defined for negative integers and $0$. I also know that differentiation and integration are inverse operators so I thought of finding $\frac{-1}{2}$th antiderivative of $f(x)=x$ so that I can find the half derivative of $x$. However it seems that it does not work. What is the problem with this? Am I missing something or is it not possible? I know some other ways of finding half derivative of $x$, so what I am asking is the problem about what I tried.  My attempt: $$\frac{1}{\Gamma\left(-\frac{1}{2}\right)} \int^x_0(x-t)^{-\frac{3}{2}}\space t\space dt=\frac{x}{2\sqrt{\pi}}\int^0_x u^{-\frac{3}{2}}\space (x-u)\space du$$  This definite integral is divergent and so I cannot get to a result. What are the best strategies for assessing if a journal is a &quot;vanity&quot; or &quot;predatory&quot; journal that should be avoided (both for publishing in and reviewing for)? For example, how would one go about determining if a journal/publisher belongs on ?