recurrence relation
Self-referential sequence definition
A recurrence relation is a mathematical equation that defines each term in a sequence using previous terms.
The Fibonacci sequence follows a recurrence relation: each number is the sum of the two before it.
Recurrence relations appear throughout computer science for analyzing algorithms and in discrete mathematics for modeling growth patterns.
Series summing consecutive terms
- geometric progressionSeries multiplying by constant
- factorialDescending multiplication of integers
- Pascal's triangleTriangular array of binomial coefficients
- Stirling numbersCounts set partitions or permutation cycles
Alike in composition throughout
- nonhomogeneousNot uniform in structure
- generating functionsPower series encoding sequences
- initial conditionsState at time zero
- boundary conditionsValues specified at limits
Overcome by fragmenting opposition
- subproblemsSmaller parts of bigger challenges
- top-downDirected from highest level
- bottom-upStarting from fundamentals
- base caseRecursion's stopping condition
Process of approaching sameness
- divergenceSeparation from common origin
- stabilityResistance to displacement
- growth rateSpeed of increase
- exponential growthQuantity multiplying proportionally over time
Fibonacci sequence
Series summing consecutive terms
- geometric progressionSeries multiplying by constant
- factorialDescending multiplication of integers
- Pascal's triangleTriangular array of binomial coefficients
homogeneous
Alike in composition throughout
- nonhomogeneousNot uniform in structure
- generating functionsPower series encoding sequences
- initial conditionsState at time zero
divide and conquer
Overcome by fragmenting opposition
- subproblemsSmaller parts of bigger challenges
- top-downDirected from highest level
- bottom-upStarting from fundamentals
convergence
Process of approaching sameness
- divergenceSeparation from common origin
- stabilityResistance to displacement
- growth rateSpeed of increase
exponential growth · oscillation · steady state · equilibrium · fixed point
- fibonacciFibonacci sequence, Fibonacci numbers, golden ratio, phi, golden spiral
- combinatoricspermutation, combinations, combination, counting, arrangements
- discrete mathcombinatorics, graph theory, set theory, number theory, proofs
- dynamic programmingtabulation, bottom-up approach, word break
- Algorithm Analysisruntime, running time, growth rate, complexity, linear
- Chebyshev polynomialsorthogonality, zeros, extrema, coefficients
relation, relationship, relations, recurring, recurrence relations, recurrent, recurrence, recurrently, recurred