Starting value

This article or the following section is not adequately provided with supporting documents ( e.g. individual evidence ). Information without sufficient evidence could be removed soon. Please help Wikipedia by researching the information and including good evidence.

In mathematics as well as in computer science in numerical and iterative processes ( algorithms ), a start value is a certain value of a variable with which a calculation is started. Similarly, in programming it is the parameter that is transferred to a routine (input value) .

It is generally customary to designate the start value by indexing the variable name with "0" (further values ​​in iterative methods with 1, 2, 3, ... , generally with "n" too natural number , otherwise also with the Name of the free, running variable ). But there are also other notations.

Examples

• ${\displaystyle x_{n+1}=x_{n}-{\tfrac {f(x_{n})}{f'(x_{n})}},}$the Newton's method for finding a zero , start value is a certain amount of estimated x coordinate that could fit about the procedure converges under certain conditions to the root. In general, the better the starting value, the faster and safer the convergence; a corresponding program line could read after a number for has been determined beforehand , which can be transferred to the function (for a certain function) as a parameter. ${\displaystyle x_{0}}$nullstelle=newton(schaetzwert)schaetzwertnewton
• ${\displaystyle f_{n}=f_{n-2}+f_{n-1},\;}$the definition of the Fibonacci sequence . As a special feature, it requires two starting values, and with it results in the basic form 1, 1, 2, 3, 5, 8,… . ${\displaystyle f_{0}}$ ${\displaystyle f_{1}}$ ${\displaystyle \{1,1\}}$
• ${\displaystyle {\vec {r}}(t)={\vec {v}}t+{\vec {r}}_{0},\;}$ uniform straight-line movement , is the starting point at a certain point in time , otherwise a function of time is noted as a function value of the free variable but usually in brackets, in practice it is also written; here the start value is a vector (in a value triple). ${\displaystyle {\vec {r}}_{0}}$ ${\displaystyle t_{0}}$ ${\displaystyle t}$ ${\displaystyle {\vec {r}}_{t}}$ ${\displaystyle \mathbb {R} ^{3}}$
• Seed key , starting value of a numerical random number generator (English seed , seed, this expression is to be found more widely in information technology in this sense of an initialization).