Search results
Results from the 24/7 Vacations Content Network
The absolute value of a number may be thought of as its distance from zero. In mathematics, the absolute value or modulus of a real number , denoted , is the non-negative value of without regard to its sign. Namely, if is a positive number, and if is negative (in which case negating makes positive), and . For example, the absolute value of 3 is ...
The condition number is derived from the theory of propagation of uncertainty, and is formally defined as the value of the asymptotic worst-case relative change in output for a relative change in input. The "function" is the solution of a problem and the "arguments" are the data in the problem. The condition number is frequently applied to ...
Examples. The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).
The term arithmetic underflow (also floating point underflow, or just underflow) is a condition in a computer program where the result of a calculation is a number of more precise absolute value than the computer can actually represent in memory on its central processing unit (CPU). Arithmetic underflow can occur when the true result of a ...
The absolute difference of two real numbers and is given by , the absolute value of their difference. It describes the distance on the real line between the points corresponding to and . It is a special case of the L p distance for all and is the standard metric used for both the set of rational numbers and their completion, the set of real ...
In mathematics, the positive part of a real or extended real -valued function is defined by the formula. Intuitively, the graph of is obtained by taking the graph of , chopping off the part under the x -axis, and letting take the value zero there. Similarly, the negative part of f is defined as. Note that both f+ and f− are non-negative ...
Norm (mathematics) In mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin. In particular, the Euclidean distance in an Euclidean ...
If is a positive number we want to represent, it will be between a machine number below and a machine number above . If x b = ( 1. b 1 b 2 … b m ) 2 × 2 k {\textstyle x_{b}=\left(1.b_{1}b_{2}\ldots b_{m}\right)_{2}\times 2^{k}} , where m {\textstyle m} is the number of bits used for the magnitude of the significand , then: