Recursions and Their Stability

  • W. Richard Kolk
  • Robert A. Lerman


Recursion formulae are algorithms in which an initial value is used to produce a new value, which in turn is inserted into the algorithm to produce again a new value, the process being repeated as many times as is desired. Jacobi’s iteration is just such a recursion, whose algorithm is the basis for solving a set of linear algebraic equations. We consider the simplest case of two such equations in two unknowns,
$$\begin{array}{*{20}{c}} {{{a}_{{11}}} \cdot {{x}_{1}} + {{a}_{{12}}} + {{x}_{2}} = {{b}_{1}}} \\ {{{a}_{{21}}} \cdot {{x}_{1}} + {{a}_{{22}}} \cdot {{x}_{2}} = {{b}_{2}}} \\ \end{array}$$


Nonlinear System Dynamics Recursion Formula Cube Root Stable Node Stable Focus 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Van Nostrand Reinhold 1992

Authors and Affiliations

  • W. Richard Kolk
    • 1
  • Robert A. Lerman
    • 2
  1. 1.PortlandUSA
  2. 2.West HartfordUSA

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