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Linear Recurrence With Constant Coefficients
In mathematics (including combinatorics, linear algebra, and dynamical systems), a linear recurrence with constant coefficients (also known as a linear recurrence relation or linear difference equation) sets equal to 0 a polynomial that is linear in the various iterates of a variable—that is, in the values of the elements of a sequence. The polynomial's linearity means that each of its terms has degree 0 or 1. A linear recurrence denotes the evolution of some variable over time, with the current time period or discrete moment in time denoted as , one period earlier denoted as , one period later as , etc. The ''solution'' of such an equation is a function of , and not of any iterate values, giving the value of the iterate at any time. To find the solution it is necessary to know the specific values (known as '' initial conditions'') of of the iterates, and normally these are the iterates that are oldest. The equation or its variable is said to be '' stable'' if from any set of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
