Combinatorics | Algebra | Recurrence relations

Recurrence relation

In mathematics, a recurrence relation is an equation according to which the th term of a sequence of numbers is equal to some combination of the previous terms. Often, only previous terms of the sequence appear in the equation, for a parameter that is independent of ; this number is called the order of the relation. If the values of the first numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In linear recurrences, the nth term is equated to a linear function of the previous terms. A famous example is the recurrence for the Fibonacci numbers, where the order is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on . For these recurrences, one can express the general term of the sequence as a closed-form expression of . As well, linear recurrences with polynomial coefficients depending on are also important, because many common elementary and special functions have a Taylor series whose coefficients satisfy such a recurrence relation (see holonomic function). Solving a recurrence relation means obtaining a closed-form solution: a non-recursive function of . The concept of a recurrence relation can be extended to multidimensional arrays, that is, indexed families that are indexed by tuples of natural numbers. (Wikipedia).

Video thumbnail

Evaluating Recurrence Relations (1 of 4: When do you apply Recurrence Relations?)

More resources available at www.misterwootube.com

From playlist Further Integration

Video thumbnail

Discrete Math - 2.4.2 Recurrence Relations

What is a recurrence relation, and how can we write it as a closed function? Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

Video thumbnail

Solve the Recurrence Relation by Backtracking: a_n = a_(n-1)

In this video I will show you how to solve a recurrence relation by using the method of backtracking. I hope this video helps someone.

From playlist Recurrence Relations

Video thumbnail

Sequences: Introduction to Solving Recurrence Relations

This video introduces solving recurrence relations by the methods of inspection, telescoping, and characteristic root technique. mathispower4u.com

From playlist Sequences (Discrete Math)

Video thumbnail

Recurrence Relation Solution - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Video thumbnail

How to Solve a Second Order Linear Homogeneous Recurrence Relation(Distinct Real Roots Case)

In this video I will show you how to solve a second order linear homogeneous recurrence relation. The problem in this video is the case with distinct real roots.

From playlist Recurrence Relations

Video thumbnail

How to Solve a Recurrence Relation using Backtracking: a_n = 2a_(n-1)

In this video I go through the steps of solving a recurrence relation using something called backtracking. This is a simple example so if you are new to this it may be useful. This is something you typically see in a discrete math class. I hope this video helps someone:)

From playlist Recurrence Relations

Video thumbnail

Discrete Math - 8.1.1 Modeling with Recurrence Relations

Modeling some of the famous combinatoric questions (Tower of Hanoi, Fibonacci) with recurrence relations. Textbook: Rosen, Discrete Mathematics and Its Applications, 7e Playlist: https://www.youtube.com/playlist?list=PLl-gb0E4MII28GykmtuBXNUNoej-vY5Rz

From playlist Discrete Math I (Entire Course)

Video thumbnail

Lecture 19.7 - Recurrence Relations

This is Lecture 19.7 of the CSE373 (Analysis of Algorithms) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1997. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/video-lectures/1997/lecture3.pdf

From playlist CSE373 - Analysis of Algorithms - 1997 SBU

Video thumbnail

Lecture 2 - Manipulating Sums

This is Lecture 2 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2002.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

Lecture 1 - Josephus Problem

This is Lecture 1 of the CSE547 (Discrete Mathematics) taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Stony Brook University in 1999. The lecture slides are available at: http://www.cs.sunysb.edu/~algorith/math-video/slides/Lecture%2001.pdf More information may

From playlist CSE547 - Discrete Mathematics - 1999 SBU

Video thumbnail

‘The’ Characteristic Equation: …An approach to Abstract Vector Spaces

#SoME1 Chapters… : 00:00 Intro 01:28 Meaning of Linear & Homogeneous 02:14 Linear, homogeneous Recurrence Relations 04:29 Finding an explicit function for linear, homogeneous Recurrence Relations 04:48 Linear, homogeneous Differential Equations with constant coefficients 05:24 Solving

From playlist Summer of Math Exposition Youtube Videos

Video thumbnail

Lecture 11 - Combinatorics

This is Lecture 11 of the COMP300E (Programming Challenges) course taught by Professor Steven Skiena [http://www.cs.sunysb.edu/~skiena/] at Hong Kong University of Science and Technology in 2009. The lecture slides are available at: http://www.algorithm.cs.sunysb.edu/programmingchallenges

From playlist COMP300E - Programming Challenges - 2009 HKUST

Video thumbnail

Discrete Math II - 8.2.4 Non-Homogeneous Linear Recurrence Relations

Our final lesson (for a bit) on solving recurrence relations introduces us to non-homogeneous recurrence relations. This occurs when, in addition to using previous values in our sequence, we also use a function of n to determine subsequent values. You should already be familiar with solvin

From playlist Discrete Math II/Combinatorics (entire course)

Video thumbnail

Lecture 18 - Introduction to Dynamic Programming

This is Lecture 18 of the CSE373 (Analysis of Algorithms) course taught by Professor Steven Skiena [http://www3.cs.stonybrook.edu/~skiena/] at Stony Brook University in 2016. The lecture slides are available at: https://www.cs.stonybrook.edu/~skiena/373/newlectures/lecture16.pdf More inf

From playlist CSE373 - Analysis of Algorithms 2016 SBU

Video thumbnail

HOMOGENEOUS RECURRENCE RELATIONS - Discrete Mathematics

Learn how to solve homogeneous recurrence relations. In this video we solve homogeneous recurrence relations. This happens when a bunch of terms add up to 0. #DiscreteMathematics #RecurrenceRelations #DiscreteMath Visit our website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.

From playlist Discrete Math 2

Video thumbnail

Recurrence Relation - Intro to Algorithms

This video is part of an online course, Intro to Algorithms. Check out the course here: https://www.udacity.com/course/cs215.

From playlist Introduction to Algorithms

Related pages

Fibonacci number | Inverse function | Logistic map | Integrodifference equation | Absolute value | Rational function | Recursion (computer science) | Characteristic polynomial | Tent map | Linear function | Bessel function | Comb filter | Continued fraction | Derivative | Abramov's algorithm | Interest rate | Linear recurrence with constant coefficients | Finite difference | Polynomial solutions of P-recursive equations | Operator (mathematics) | Initial condition | Infinite impulse response | Rational difference equation | Factorial | Special functions | Holonomic function | Sequence | Petkovšek's algorithm | Generating function | Iterated function | Equation | Combinatorial principles | Natural number | Binary search algorithm | Binomial coefficient | Function (mathematics) | Closed-form expression | Mathematics | Discretization | Chaos theory | Ordinary differential equation | Mathematical induction | Pascal's triangle | Taylor series | Dyadic transformation | Initial value problem | Stability theory | Limit of a sequence | Time complexity | Digital signal processing | Integral equation | Tuple | P-recursive equation | Summation equation | Orthogonal polynomials | Integration by reduction formulae | Lagged Fibonacci generator | Linear differential equation | Algorithm | Analysis of algorithms | Matrix difference equation | Recursion | Master theorem (analysis of algorithms) | Digital filter