Concepts inMore efficient computation of the complex error function
Error function
In mathematics, the error function (also called the Gauss error function) is a special function of sigmoid shape which occurs in probability, statistics and partial differential equations. It is defined as: (When x is negative, the integral is interpreted as the negative of the integral from x to zero.
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Efficiency (statistics)
In statistics, efficiency is a term used in the comparison of various statistical procedures and, in particular, it refers to a measure of the optimality of an estimator, of an experimental design or of an hypothesis testing procedure. Essentially, a more efficient estimator, experiment or test needs fewer samples than a less efficient one to achieve a given performance.
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Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis. It can be thought of as a modified Cartesian plane, with the real part of a complex number represented by a displacement along the x-axis, and the imaginary part by a displacement along the y-axis. The concept of the complex plane allows a geometric interpretation of complex numbers. Under addition, they add like vectors.
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Approximation error
The approximation error in some data is the discrepancy between an exact value and some approximation to it. An approximation error can occur because the measurement of the data is not precise due to the instruments. (e.g. , the accurate reading of a piece of paper is 4.5cm but since the ruler does not use decimals, you round it to 5cm. ) or approximations are used instead of the real data (e.g. , 3.14 instead of ¿).
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Significant figures
The significant figures (also called significant digits or, informally, 'sig figs') of a number are those digits that carry meaning contributing to its precision. This includes all digits except: leading and trailing zeros which are merely placeholders to indicate the scale of the number. spurious digits introduced, for example, by calculations carried out to greater precision than that of the original data, or measurements reported to a greater precision than the equipment supports.
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Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length. Each reference line is called a coordinate axis or just axis of the system, and the point where they meet is its origin, usually at ordered pair (0,0).
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