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Topic: Recurrence relation

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	[No title] (Site not responding. Last check: 2007-10-21)
		It is an object of the present invention to utilize a recurrence relation and output equation having distinct pair distances.
		In addition, the order k of the recurrence relation which encodes the same amount of states is reduced by a factor of n, or 8 for GF In the present invention, a maximal length recurrence relation is utilized for optimal results.
		For a recurrence relation, the output element is generated from a linear function of the state of the register and the coefficients, as defined by equation (1).
	www.wipo.int /cgi-pct/guest/getbykey5?KEY=99/22484.990506&ELEMENT_SET=DECL (7997 words)

	[No title]
		For example, the recurrence relation g(n) = g(n-1) + 2n -1 g(0) = 0 defines the function f(n) = n^2, and the recurrence relation f(n) = f(n-1) + f(n-2) f(1) = 1 f(0) = 1 defines the famous Fibanocci sequence 1,1,2,3,5,8,13,....
		Recurrence relations with more than one variable: In some applications we may consider recurrence relations with two or more variables.
		To solve this recurrence relation, we would have to use a more sophisticated technique for linear homogeneous recurrence relations, which is discussed in the text book for Math112.
	www.cs.ucr.edu /~jiang/cs141/recur-tut.txt (419 words)

	Why and how
		These are (i) recurrence relations as general ways to see what happens between consecutive terms of a sequence; and (ii) the general term of a sequence as a function of the number of that term.
		And one final note on recurrence relations of the type we are dealing with here, if we know the recurrence relation of a sequence and we know its first term, then we know the sequence completely.
		The point that we are trying to make is that recurrence relations should be grounded in the actual physical problem and not in a table of values that may be guessed from small values of the physical pattern.
	www.nzmaths.co.nz /algebra/units/whyandhow.htm (2905 words)

	Sapphire: Efficient prototyping of recurrences
		Recurrence relations is the mathematical form used to express many important problems.
		Recurrence relations form the core of a computational model of a PDE. For many problems, such as those in computational fluid dynamics, formulating an appropriate recurrence relation is a non-trivial task.
		The natural way of expressing a recurrence relation in a programming language such as C++ would be as recursive function calls mimicing the recursive equations from the mathematical formulation.
	www.ii.uib.no /saga/SC96EPR (935 words)

	Recurrence Relations (Site not responding. Last check: 2007-10-21)
		Recurrence Relations are another means of defining a sequence of numbers.
		Recurrence relations define a term of the sequence in terms of previous terms of the sequence and, possibly, other functions of n.
		Although the methods given above find correct solutions to recurrence relations some caution must be exercised in applying the methods blindly since there are some important nuances in the theory behind the methods and the theory has not been covered here.
	cs-netlab-01.lynchburg.edu /courses/Algorithms/recurenc.htm (2084 words)

	CmSc 180 Discrete Mathematics
		Recursion is the presence of a recurrence relation for a given sequence
		Any recurrence relation is accompanied by initial condition (sometimes called terminating condition) which specifies the first term of the sequence.
		Be able to recognize patterns in a given sequence of numbers and write down the recurrence relation between its terms.
	www.simpson.edu /~sinapova/cmsc180-02/L16-Recursion.htm (271 words)

	PlanetMath: Stirling numbers of the second kind
		The recursive point of view, therefore explains the connection between the recurrence formula, and the original definition.
		Since this relation holds for all polynomials, it also holds for all formal power series.
		Cross-references: section, formal power series, relation, sides, simple, solution, differential equation, operators, derivative, matrix, generate, powers, monomial, infinite-dimensional, basis, obvious, indeterminate, polynomials, vector space, between, connection, recursive, division, one way, formula, initial conditions, terms, differential operators, falling factorial, generating function, recurrence relation, groups, partition, Stirling number, characterizations, equivalent, properties, natural numbers, sequence
	planetmath.org /encyclopedia/StirlingNumbersSecondKind.html (530 words)

	[No title]
		For formula like these, called recurrence relations, it is desired to find a unique solution, a solution expressed only in terms of n, so that any number of the sequence can be calculated directly.
		In general The general solution of the a recurrence relation of the form an+1 = dan, where n(0, d constant, and a0 = A is unique and given by: an = a0dn = Adn, n(0 This then is a discrete function whose domain is N, the set of positive integers.
		The final recurrence is the total number of all subsets that contain "n" (an-2) and those that don't contain "n" (an-1), and we have an = an-2 + an-1.
	www.utdallas.edu /~cshields/teach/discrete_summ99/notes/discrete2_student_recrelation.doc (3888 words)

	IST230 – More Counting Techniques
		Relational data model was developed to represent databases of information with, potentially thousands and millions of data that would need to be added, updated, deleted and manipulated on a daily basis.
		Equivalence relation is a relation on a set A that is reflexive, symmetric and transitive.
		Equivalence classes: In an equivalence relation (R) on a set A, the set of all elements that are related to an element a of A is called the equivalence class of a.
	www.personal.psu.edu /faculty/p/l/pld2/ist230fall01/ch5and6.htm (1415 words)

	Research topics, recurrence relations
		Such a recurrence relation is especially suitable for calculating these functions for successive values of a parameter.
		In many cases however the wanted solution is dominated by other solutions of the recurrence relation, and so forward computation of the solution is not a stable process.
		Research in the department concentrates on the development of algorithms for the stable evaluation of non-dominant solutions of linear recurrence relations and recurrence systems, and on the acceleration of the convergence of existing algorithms.
	www.cs.kuleuven.ac.be /~ade/nalag/research/topics/recur.shtml (92 words)

	cs504 Class 5
		Recurrence relations describe how one element of a sequence can be computed from one or more of the previous elements in the sequence.
		There is no one way to solve recurrence relations, but they do come in families - in that respect they are similar to their analogue in continuous mathematics, the differential equation.
		Every summation has an implicit recurrence relation which can be found by using the first step of the perturbation method for solving summations.
	www.cs.wpi.edu /~cs504/s99/classes/class05/class05.html (1173 words)

	Chapter 3 Key Terms
		A recurrence relation of degree k for a sequence {a
		A solution to a recurrence relation is a sequence that satisfies the recurrence relation.
		The solution to this recurrence relation (and initial condition) is H
	astro.temple.edu /~stafford/cis66s02/chap5/c5s1.htm (271 words)

	Recurrence Relations
		A recurrence relationship is a rule by which a sequence is generated.
		Find a recurrence relation and give initial conditions for the number of bit strings of length n that do not have two consecutive 0s.
		Set up a recurrence relation for the number of cars produced in the first n months by this factory.
	web1.cs.montana.edu /defrance/courses/Fall_01/cs223/lecture/recurrence.html (781 words)

	Some Details About the Parma Recurrence Relation Solver
		It is more difficult to characterize completely the set of such recurrences that have a solution in closed form: PURRS will attempt to express the solution using polynomials, exponentials and factorials, or a suitable combination of the same functions.
		These are recurrences of the form x(n) = a * x(n/b) + p(n), where a is positive, b > 1 and p(n) is a function whose domain is the set of positive integers, and the value n/b is always understood as its integer part.
		A typical example of this class is the recurrence satisfied by the worst-case complexity of the merge-sort algorithm.
	www.cs.unipr.it /purrs/details (1692 words)

	Big-Oh for Recursive Functions: Recurrence Relations
		When you write a recurrence relation you must write two equations: one for the general case and one for the base case.
		So we've solved the recurrence relation and its solution is what we "knew" it would be.
		The recurrence relation for the average case is
	www.cs.duke.edu /~ola/ap/recurrence.html (1255 words)

	Discrete Mathematics -- Quiz 2 Whiteley -- Fall 1996 (Site not responding. Last check: 2007-10-21)
		Consider the recurrence relation: a_n = a_{n-1} + 2(n+1)$ for n >= 1, with the initial condition a_0= 2.
		Substituting the answer in the recurrence relation: LHS = (3)^n - (-1)^n = 9[3^(n-2)] - (-1)^(n-2) RHS = 2[(3)^(n-1) - (-1)^(n-1)] + 3[(3)^(n-2) - (-1)^(n-2)] = 6[3^(n-2)] + 2(-1)^(n-2)] + 3[(3)^(n-2)] -3(-1)^(n-2)] = 9[3^(n-2)] - 1 (-1)^(n-2)] = LHS!
		Recurrence relations with appropriate initial conditions always have a unique sequence as a solution (something we proved by induction).
	www.math.yorku.ca /Courses/9697/Math2320/q3w.html (508 words)

	ICS141 Lecture Notes #23 (04/16/98) (Site not responding. Last check: 2007-10-21)
		A recurrence relation (or recurrence equation) of a function f ^^^^^^^^^^^^^^^^^^^ ^^^^^^^^^^^^^^^^^^^ on the domain N is an inductive definition of f that is of the form f(n) = g(n, f(n-1), f(n-2),...
		A recurrence relation for a specific value of n is called an initial condition (or boundary condition).
		A sequence satisfying a recurrence system without initial conditions is called a general solution of the recurrence system.
	www2.ics.hawaii.edu /~sugihara/course/ics141s98/note/04-16n23 (779 words)

	Multidimensional Recurrence Relation
		Certainly the zero polynomial is a recurrence relation for any sequence s.
		Computing a minimal generator of the ideal is equivalent to finding the shortest recurrence relation for s.
		are all recurrence relations for s, then the shaded region in Figure 16.3 represents all entries of sthat can be generated by them.
	www.math.clemson.edu /faculty/Gao/calg/node17.html (374 words)

	Recurrence relations
		, is an equation that relates an to certain of its predecessors a
		The Tower of Hanoi is a puzzle consisting of three pegs mounted on a board and n disks of various sizes with holes in their centers.
		A linear homogeneous recurrence relation of order k with constant coefficients is a recurrence relation of the form :
	condor.depaul.edu /~ichu/csc415/notes/notes5/lecture5.html (290 words)

	CS494 Computational Geometry: Algorithm Analysis Practice
		The best way to analyze the running time of such a function (or algorithm) is to write a recurrence relation that represents the running time.
		For now we are concerned with determining the recurrence relation from code or pseudo-code.
		The recurrence relation is an intermediate step in the process of determining the big-O running time of an algorithm.
	www.cs.utk.edu /~booth/494-02/notes/alganalpractice.html (2356 words)

	New Page 2 (Site not responding. Last check: 2007-10-21)
		Example of a problem that needs recurrence relations to be expressed is:
		recurrence relation of degree k with constant coefficient is a recurrence relation of the form
		When s is not a root of the characteristic equation of the associated linear homogeneous recurrence relation, there is a particular solution of the form: (p
	www.cis.temple.edu /~assoul/6.1_6.2_6.5.htm (703 words)

	Discrete mathematics:Recursion - Wikibooks, collection of open-content textbooks
		The number j is important, and it is known as the order of the linear recurrence relation.
		Because we have a second order recurrence, the general solution is the sum of two solutions, corresponding to the two roots of the characteristic equation.
		The characteristic equation of this recurrence relation is
	en.wikibooks.org /wiki/Discrete_mathematics:Recursion (1013 words)

	fibonacci
		One of the most famous recurrence relations occuring in all of mathematics is the sequence of numbers satisfying
		The solutions of homogeneous linear recurrence relations using this technique obviously depends on finding distinct roots of polynomial equations, which can be a difficult problem in its own right.
		Many recurrence relations must be solved using more sophisticated techinques, such as creating generating functions, that we do not discuss here.
	www-math.cudenver.edu /~rrosterm/fibonacci/fibonacci.html (960 words)

	[No title]
		T is an example of a recurrence relation, i.e., the value of T for a specific argument n is defined in terms of values of T for arguments < n.
		A mathematically interesting method for finding the closed form expression for a recurrence relation is to use the idea of a generating function.
		Since the generating function of a recurrence relation is unique, we have
	www.ececs.uc.edu /~gpurdy/lec5.html (551 words)

	Neptune Cycle · Astrological definition of Neptune Cycle · Astrology Encyclopedia
		Their recurrence of relation, a cycle of aspect that is known as the synodic cycle, has a mean value of 492 1/3 years, although now and for a long time to come it is nearer 493½ years.
		This can be related to the 3,100-year period of 3 conjunctions of the two outermost planets, in which time they return not only to the same relation, but also to nearly the same position in the Zodiac.
		Bradford's five phases equal 1,250 years, approximately the period of Pluto's position and relation recurrence with the planet just beyond it, it appears to indicate that her study is actually an observation of the effects of the cycles of the four outermost planets - even though she herself is not an astrologer.
	www.astrologyweekly.com /dictionary/neptune-cycle.php (1013 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		an equation that relates an element of a sequence to certain of its predecessors, and
		it is often easy to create a recursive algorithm to address a problem if the recurrence relation for the problem is known
		Recurrence relation for counting the number of n-bit strings that do not contain the pattern 111
	www.people.vcu.edu /~dprimeau/cmsc301/sp99/notes5.html (63 words)

	Tower of Hanoi
		The above expression is known as a recurrence relation which, as you might have noticed, is but a recursive function.
		Other recurrence relations may be more complicated, for example,
		Recurrence relations appear under various guises in numerous branches of Mathematics and applications.
	www.cut-the-knot.org /recurrence/hanoi.shtml (762 words)

	cs504 Class 4
		See the discussion n the Recurrence Relation Notes on the Notes page.
		However, we can note that moving a stack of N rings has three stages: move the top N-1 rings to the third rod, move the N-th ring to the second rod, move the N-1 smaller rings to sit on top of the N-th ring.
		The recurrence relation for the number of comparisons is:
	www.cs.wpi.edu /~cs504/s00m/classes/class04/Class04.html (2297 words)

	BSSA, Volume 95:1 (Site not responding. Last check: 2007-10-21)
		An important component of seismic hazard analysis is the magnitude-recurrence relation, which provides the cumulative rate of occurrence of earthquakes within a seismic source zone as a function of magnitude.
		Perhaps more importantly, the use of a homogeneous catalog reduces the uncertainty in the recurrence rates of moderate to large earthquakes in CASR by nearly an order of magnitude.
		We conclude that the use of a homogeneous magnitude scale is critical to producing unbiased magnitude-recurrence relations.
	www.seismosoc.org /publications/BSSA_html/bssa_95-1/04095.html (275 words)

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