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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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 π).
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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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Calculation
A calculation is a deliberate process for transforming one or more inputs into one or more results, with variable change. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm to the vague heuristics of calculating a strategy in a competition or calculating the chance of a successful relationship between two people. For example, multiplying 7 by 8 is a simple algorithmic calculation.
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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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Complex number
A complex number is a number which can be put in the form a + bi, where a and b are real numbers and i is called the imaginary unit, where . In this expression, a is called the real part and b the imaginary part of the complex number. Complex numbers extend the idea of the one-dimensional number line to the two-dimensional complex plane by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number can be identified with the point (a, b).
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Accuracy and precision
In the fields of science, engineering, industry and statistics, the accuracy of a measurement system is the degree of closeness of measurements of a quantity to that quantity's actual (true) value. The precision of a measurement system, also called reproducibility or repeatability, is the degree to which repeated measurements under unchanged conditions show the same results.
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