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Topic: Big O notation


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  Big O notation - Wikipedia, the free encyclopedia
Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
Big O notation is useful when analyzing algorithms for efficiency.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
www.cs.waikato.ac.nz /Teaching/COMP317B/Week_1/Big_o_notation.html   (1649 words)

  
  Big O notation
Big O notation (with a capital letter O -- originally an omicron -- not a zero), also called Landau's symbol, is a symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of functions.
Obviously, this notation is abusing the equality symbol, since it violates the axiom of equality: "things equal to the same thing are equal to each other".
In addition to the big O notations, another Landau symbol is used in mathematics: the little o.
www.teachersparadise.com /ency/en/wikipedia/b/bi/big_o_notation.html   (907 words)

  
  Big O notation
Big O notation or Big Oh notation, and also Landau notation or asymptotic notation, is a mathematical notation used to describe the asymptotic behavior of functions.
Big O can also be used to describe the error term in an approximation to a mathematical function.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
www.brainyencyclopedia.com /encyclopedia/b/bi/big_o_notation.html   (2036 words)

  
  Big O notation - Biocrawler   (Site not responding. Last check: )
The Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
Big O notation is useful when analyzing algorithms for efficiency.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
www.biocrawler.com /encyclopedia/Big-O   (1160 words)

  
  Big O notation - Wikipedia, the free encyclopedia
Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
Big O can also be used to describe the error term in an approximation to a mathematical function.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
en.wikipedia.org /wiki/Big_O_notation   (1709 words)

  
 Big O notation   (Site not responding. Last check: )
Big O notation is a type of symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of functionss.
The O was originally a capital omicron; today the capital letter O is used, but never the digit zero.
Big O is the most commonly used asymptotic notation for comparing functions.
www.encyclopedia-1.com /b/bi/big_o_notation.html   (981 words)

  
 Big O notation - the free encyclopedia   (Site not responding. Last check: )
In complexity theory, computer science, and mathematics, the Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
Big O notation is useful when analyzing algorithmsfor efficiency.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informalsubstitute for Θ (see below).
www.free-web-encyclopedia.com /default.asp?t=Big_O_notation   (937 words)

  
 Kids.Net.Au - Encyclopedia > Big O notation
Big O notation (with a capital letter O, not a zero), also called Landau's symbol, is a symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of functions.
Obviously, this notation is abusing the equality symbol, since it violates the axiom of equality: "things equal to the same thing are equal to each other".
In addition to the big O notations, another Landau symbol is used in mathematics: the little o.
www.kids.net.au /encyclopedia-wiki/bi/Big_O_notation   (868 words)

  
 Landau notation - Wikipedia, the free encyclopedia
In complexity theory, computer science, and mathematics, Landau notation, also called "little o"- and "big O notation", is a mathematical notation used for asymptotic comparison of functions.
The advantage of the above notation is that it allows for the abuse of notation consisting in writing f = g + o(h) instead of f - g = o(h), which is quite handy in calculations of approximations obtained by (repeated) use of Taylor's theorem and formulae for this notation (see below).
Main applications of Landau notations are found in complexity theory and asymptotic analysis.
en.wikipedia.org /wiki/Landau_notation   (774 words)

  
 Bambooweb: Big O notation
Big O notation is a type of symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of functions.
The O was originally a capital omicron; today the capital letter O is used, but never the digit zero.
Big O is the most commonly used asymptotic notation for comparing functions.
www.bambooweb.com /articles/b/i/Big_O_notation.html   (997 words)

  
 PlanetMath: Landau notation
In analysis, such notation is useful in describing error estimates.
O notation, omega notation, theta notation, big-O notation
This is version 15 of Landau notation, born on 2001-10-06, modified 2006-09-21.
planetmath.org /encyclopedia/LandauNotation.html   (184 words)

  
 Big Oh
Big O notation immediately tells you there's no point doing a detailed analysis or timing measurement, much less writing it in assembly language -- it's going to take over a hundred years, even if you could get the inner loop to run in 1 clock cycle.
Big O notation expresses the asymptotic (for large N) behavior of an algorithm.
Thus, though Big O is a powerful tool that a performance tuner must both acknowledge and understand, life is rarely so simple in practice.
c2.com /cgi/wiki?BigOh   (1981 words)

  
 Landau notation - Definition, explanation
In complexity theory, computer science, and mathematics, Landau notation, also called "little o"- and "big O notation", is a mathematical notation used for asymptotic comparison of functions.
The advantage of the above notation is that is allows for the abuse of notation consisting in writing f = g + o(h) instead of f - g = o(h), which is quite handy in calculations of approximations obtained by (repeated) use of Taylor's theorem and formulae for this notation (see below).
Big O notation: more explicit definitions for real valued functions, explanations, and properties of these and related notations.
www.calsky.com /lexikon/en/txt/l/la/landau_notation.php   (604 words)

  
 Big O notation - ExampleProblems.com
Big O notation is a mathematical notation used to describe the asymptotic behavior of functions.
The big-O, standing for "order of", was originally a capital omicron; today the capital letter O is used, but never the digit zero.
Big O is the most commonly used asymptotic notation for comparing functions, although it is often actually an informal substitute for Θ (Theta, see below).
www.exampleproblems.com /wiki/index.php/Big_O_notation   (1055 words)

  
 InfoDense - Web - O Notation
In informal usage, the O notation is commonly employed to describe an...
Notation for differentiation, common representations of the derivative in calculus.
Big O notation, used for example in analysis to represent less significant...
www.infodense.com /topic?i=O%20Notation   (217 words)

  
 Big O notation   (Site not responding. Last check: )
Big O notation is a type of symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of function s.
The O was originally a capital omicron ; today the capital letter O is used, but never the digit zero.
The notation can also be used to describe the behavior of f near some real number a : we say : f''(''x) is O(g''(''x)) as x → a if and only if :there exists numbers δ> 0 and M such that
www.serebella.com /encyclopedia/article-Big_O_notation.html   (1426 words)

  
 Big-oh notation@Everything2.com
This notation is used as a measure of complexity.
Big-oh notation is a way of describing the change in how long an algorithm will take to run based on the number of input values it must process.
Big-oh notation is useful when comparing the efficiency of various sorting and searching algorithms to one another.
www.everything2.com /index.pl?node=Big-oh%20notation   (795 words)

  
 Eternally Confuzzled - Asymptotic Notation
A common notation that removes constants is called Big O Notation, where the O means “order of” (there are variants that do something similar that we'll look at shortly).
Big O notation refers to the asymptotic upper bound, which means that it's a cap on how much the time complexity will grow.
There's a notation for the asyptotically tight bound too, called Theta, and since we know the O and Ω for binary search and they're the same, we can say that binary search is Θ(log N).
www.eternallyconfuzzled.com /arts/jsw_art_bigo.aspx   (1909 words)

  
 Math Forum - Ask Dr. Math   (Site not responding. Last check: )
First of all, the math sense for the big-O notation is as in f(x) = x^2 + O(x) it means that there is some leftover part whose size is about (rather, not bigger than about) the function in parentheses.
As described on MathWorld at Asymptotic Notation http://mathworld.wolfram.com/AsymptoticNotation.html this means that the O(x) represents some unknown function which is smaller than some constant multiple of x.
Notice that the big-O notation says "some constant multiple of" without saying what the constant is. This leaves out some information that is sometimes important, but it allows you to talk about time without reference to the speed of your computer and without measuring exactly how many instructions are in a certain block of code.
www.mathforum.org /library/drmath/view/66806.html   (525 words)

  
 Learn more about Big O notation in the online encyclopedia.   (Site not responding. Last check: )
Big O notation (with a capital letter O -- originally an omicron -- not a zero), also called Landau's symbol, is a symbolism used in complexity theory, computer science, and mathematics to describe the asymptotic behavior of functions.
Obviously, this notation is abusing the equality symbol, since it violates the transitivity axiom of equality: "things equal to the same thing are equal to each other", as well as symmetry: the notation O(g(x)) = f(x) looks pretty strange.
Under this convention, it is said, e.g., that f(x) belongs to class (or set) O(g(x)) and the corresponding set membership notation is used.
www.onlineencyclopedia.org /b/bi/big_o_notation.html   (991 words)

  
 Mathematical Notation: Past and Future
By the way, even though math notation hadn't gotten going very well by their time, the kind of symbolic notation used in alchemy, astrology, and music pretty much had been developed.
Actually, he thought that having the right notation was somehow the secret to a lot of issues of human affairs in general.
In particular, it emphasized using notation whenever one could, and somehow minimizing the amount of potentially imprecise text that had to be written.
www.stephenwolfram.com /publications/talks/mathml/mathml2.html   (4335 words)

  
 E
One way to derive these formulas is the big O notation.
Big O notation, also called an efficiency indicator, is used to describe the growth rate of a function.
The big O notation represents the running time needed to solve the computational steps.
members.tripod.com /mishra_ruchi/bigo.htm   (1231 words)

  
 Big-O Notation and Algorithm Analysis
Now that we have seen the basics of big-O notation, it is time to relate this to the analysis of algorithms.
For example, when we are analyzing an algorithm that multiplies two numbers, the functions we might be interested in are the relationships between the number of digits in each number and the length of time or amount of memory required by the algorithm.
Although big-O notation is a way of describing the order of a function, it is also often meant to represent the time complexity of an algorithm.
www.eecs.harvard.edu /~ellard/Q-97/HTML/root/node8.html   (876 words)

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