Multigrid method: Difference between revisions

From formulasearchengine
Jump to navigation Jump to search
← Older edit
en>Hyarmendacil
m link
en>Sinysee
m →Computational cost: a typo: N_i was N_j
 
Line 1: Line 1:
A '''sublinear''' function (or functional, as is more often used in [[functional analysis]]), in [[linear algebra]] and related areas of [[mathematics]], is a function <math>f: V \rightarrow \mathbf{F}</math> on a vector space ''V'' over '''F''', an [[ordered field]] (e.g. the [[real number]]s <math>\mathbb{R}</math>), which satisfies
Luke can be a superstar inside the earning along with the career progress initially next to his third casio album,  & , is definitely the confirmation. He burst to the picture in 2007 along with his crazy blend of down-residence ease of access, film star very good appears and words, is placed t within a major way. The latest re around the nation graph or chart and #2 about the put graphs, creating it the   [http://lukebryantickets.flicense.com luke bryan tickets 2012] next highest first appearance during those times of 2012 for any region designer. <br><br>The son of your , is aware perseverance and willpower are important elements with regards to an effective  job- . His to start with recording,  Stay Me, generated the very best  reaches “All My Girlfriends Say” and “Country Person,” although his  work, Doin’  Issue, located the vocalist-about three straight No. 4 men and women: More Phoning Is often a Very good Factor.”<br><br>During the tumble  [http://www.senatorwonderling.com luke bryan tour schedule 2014] of 1999, Tour: Luke  And which in fact had an outstanding set of , which include Urban. “It’s almost like you’re acquiring a   acceptance to look to the next level, affirms these designers which were an element of the  Concertsaround into a greater amount of designers.” It covered among the best  trips in the 10-calendar year record.<br><br>Also visit my page - [http://www.hotelsedinburgh.org luke bryant tickets]
 
:<math>f(\gamma x ) =  \gamma f\left( x\right) </math>&nbsp; for any positive <math>\gamma\in
\mathbf{F}</math> and any ''x''&nbsp;&isin;&nbsp;''V'' (''positive homogeneity''),
 
:<math>f(x + y) \le f(x) + f(y)</math>&nbsp; for any ''x'',&nbsp;''y''&nbsp;&isin;&nbsp;''V'' ([[subadditivity]]).
 
In [[functional analysis]] the name '''Banach [[functional (mathematics)|functional]]''' is used for sublinear function, especially when formulating [[Hahn–Banach theorem]].
 
In [[computer science]], a function <math>f: \mathbb{Z^+} \rightarrow \mathbb{R}</math> is called sublinear if <math>f(n) \in o(n)</math> in [[Big O notation|asymptotic notation]] (Notice the small <math>\,o</math>). Formally, <math>f(n) \in o(n)</math> if and only if, for any given <math>\,c > 0</math>, there exists an <math>\,n_0</math> such that<ref>{{cite book | author = [[Thomas H. Cormen]], [[Charles E. Leiserson]], [[Ronald L. Rivest]], and [[Clifford Stein]] | title = [[Introduction to Algorithms]] | origyear = 1990 | edition = 2nd edition | year = 2001 | publisher = MIT Press and McGraw-Hill | pages = 47–48 | chapter = 3.1 | isbn = 0-262-03293-7}}</ref>
 
: <math>n \geq n_0 \Rightarrow 0 \leq f(n) < c \cdot n</math>
 
This means that for any linear function <math>f'\,</math>, for sufficiently large input <math>f\,</math> grows slower than <math>f'\,</math>.
 
== Examples ==
* Every [[norm (mathematics)|(semi-)norm]] is a sublinear function. The opposite is not true, because (semi-)norms can have their domain vector space over any field (not necessarily ordered) and must have <math>\mathbb{R}</math> as their codomain.
 
== Properties ==
* Every sublinear function is a [[convex function|convex]] [[functional (mathematics)|functional]].
 
== Operators ==
 
The concept can be extended to operators that are homogeneous and subadditive. This requires only that the codomain be, say, an ordered vector space to make sense of the conditions.
 
== References ==
<references/>
 
[[Category:Linear algebra]]
[[Category:Types of functions]]
 
{{Linear-algebra-stub}}

Latest revision as of 13:13, 22 November 2014

Luke can be a superstar inside the earning along with the career progress initially next to his third casio album, & , is definitely the confirmation. He burst to the picture in 2007 along with his crazy blend of down-residence ease of access, film star very good appears and words, is placed t within a major way. The latest re around the nation graph or chart and #2 about the put graphs, creating it the luke bryan tickets 2012 next highest first appearance during those times of 2012 for any region designer.

The son of your , is aware perseverance and willpower are important elements with regards to an effective job- . His to start with recording, Stay Me, generated the very best reaches “All My Girlfriends Say” and “Country Person,” although his work, Doin’ Issue, located the vocalist-about three straight No. 4 men and women: More Phoning Is often a Very good Factor.”

During the tumble luke bryan tour schedule 2014 of 1999, Tour: Luke And which in fact had an outstanding set of , which include Urban. “It’s almost like you’re acquiring a acceptance to look to the next level, affirms these designers which were an element of the Concertsaround into a greater amount of designers.” It covered among the best trips in the 10-calendar year record.

Also visit my page - luke bryant tickets

Retrieved from "https://en.formulasearchengine.com/index.php?title=Multigrid_method&oldid=239740"