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Numerical Analysis
Numerical analysis
Numerical analysis
is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). One of the earliest mathematical writings is a Babylonian tablet from the Yale Babylonian Collection
Yale Babylonian Collection
(YBC 7289), which gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square. Being able to compute the sides of a triangle (and hence, being able to compute square roots) is extremely important, for instance, in astronomy, carpentry and construction.[2] Numerical analysis
Numerical analysis
continues this long tradition of practical mathematical calculations
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YBC 7289
YBC 7289
YBC 7289
is a Babylonian clay tablet in the Yale Babylonian Collection, notable for containing an accurate sexagesimal approximation to the square root of 2, the length of the diagonal of a unit square. It is believed to come from southern Mesopotamia
Mesopotamia
from some time in the range from 1800–1600 BC.[1][2] Its significance was first recognized by Neugebauer & Sachs (1945).[1][3]Contents1 Content 2 Interpretation 3 Provenance and curation 4 ReferencesContent[edit] The tablet depicts a square with its two diagonals. One side of the square is labeled with the sexagesimal number 30. The diagonal of the square is labeled with two sexagesimal numbers. The first of these two, 1;24,51,10 represents the number 305470/216000 ≈ 1.414213, an accurate numerical approximation of the square root of two
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NIST
The National Institute of Standards and Technology
Technology
(NIST) is a measurement standards laboratory, and a non-regulatory agency of the United States Department of Commerce
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Numerical Weather Prediction
Numerical weather prediction
Numerical weather prediction
(NWP) uses mathematical models of the atmosphere and oceans to predict the weather based on current weather conditions. Though first attempted in the 1920s, it was not until the advent of computer simulation in the 1950s that numerical weather predictions produced realistic results. A number of global and regional forecast models are run in different countries worldwide, using current weather observations relayed from radiosondes, weather satellites and other observing systems as inputs. Mathematical models based on the same physical principles can be used to generate either short-term weather forecasts or longer-term climate predictions; the latter are widely applied for understanding and projecting climate change
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Square Root Of 2
The square root of 2, or the (1/2)th power of 2, written in mathematics as √2 or 2​1⁄2, is the positive algebraic number that, when multiplied by itself, gives the number 2. Technically, it is called the principal square root of 2, to distinguish it from the negative number with the same property. Geometrically the square root of 2 is the length of a diagonal across a square with sides of one unit of length; this follows from the Pythagorean theorem. It was probably the first number known to be irrational. The rational approximation of the square root of two, 665,857/470,832, derived from the fourth step in the Babylonian algorithm starting with a0 = 1, is too large by approx. 6988160000000000000♠1.6×10−12: its square is 7000200000000000450♠2.0000000000045… The rational approximation 99/70 (≈ 1.4142857) is frequently used. Despite having a denominator of only 70, it differs from the correct value by less than 1/10,000 (approx. 6995720000000000000♠+0.72×10−4)
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Hedge Fund
A hedge fund is an investment fund that pools capital from accredited individuals or institutional investors and invests in a variety of assets, often with complex portfolio-construction and risk-management techniques.[1] It is administered by a professional investment management firm, and often structured as a limited partnership, limited liability company, or similar vehicle.[2][3] Hedge funds are generally distinct from mutual funds, as their use of leverage is not capped by regulators, and distinct from private equity funds, as the majority of hedge funds invest in relatively liquid assets.[4][5] The term "hedge fund" originated from the paired long and short positions that the first of these funds used to hedge market risk. Over time, the types and nature of the hedging concepts expanded, as did the different types of investment vehicles
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Operations Research
Operations research
Operations research
(British English: operational research) (OR) is a discipline that deals with the application of advanced analytical methods to help make better decisions.[1] Further, the term operational analysis is used in the British (and some British Commonwealth) military as an intrinsic part of capability development, management and assurance
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Actuary
An actuary is a business professional who deals with the measurement and management of risk and uncertainty (BeAn Actuary
Actuary
2011a). The name of the corresponding field is actuarial science. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills (BeAn Actuary
Actuary
2011b). Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms (Trowbridge 1989, p. 7). While the concept of insurance dates to antiquity (Johnston 1903, §475–§476, Loan 1992, Lewin 2007, pp
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Linear Interpolation
In mathematics, linear interpolation is a method of curve fitting using linear polynomials to construct new data points within the range of a discrete set of known data points.Contents1 Linear interpolation
Linear interpolation
between two known points 2 Interpolation of a data set 3 Linear interpolation
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Lagrange Polynomial
In numerical analysis, Lagrange polynomials are used for polynomial interpolation. For a given set of points ( x j , y j ) displaystyle (x_ j ,y_ j ) with no two x j displaystyle x_ j values equal, the Lagrange polynomial
Lagrange polynomial
is the polynomial of lowest degree that assumes at each value x j displaystyle x_ j the corresponding value y j displaystyle y_ j (i.e. the functions coincide at each point)
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Mechanical Calculator
A mechanical calculator, or calculating machine, is a mechanical device used to perform automatically the basic operations of arithmetic. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obsolete by the advent of the electronic calculator. Surviving notes from Wilhelm Schickard
Wilhelm Schickard
in 1623 reveal that he designed and had built the earliest of the modern attempts at mechanizing calculation. His machine was composed of two sets of technologies: first an abacus made of Napier's bones, to simplify multiplications and divisions first described six years earlier in 1617, and for the mechanical part, it had a dialed pedometer to perform additions and subtractions
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Numerical Method
In numerical analysis, a numerical method is a mathematical tool designed to solve numerical problems. The implementation of a numerical method with an appropriate convergence check in a programming language is called a numerical algorithm.Contents1 Mathematical definition 2 Consistency 3 Convergence 4 ReferencesMathematical definition[edit] Let F ( x , y ) = 0 displaystyle F(x,y)=0 be a well-posed problem, i.e
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Riemann Sum
In mathematics, a Riemann sum
Riemann sum
is a certain kind of approximation of an integral by a finite sum. It is named after nineteenth century German mathematician Bernhard Riemann. One very common application is approximating the area of functions or lines on a graph, but also the length of curves and other approximations. The sum is calculated by dividing the region up into shapes (rectangles, trapezoids, parabolas, or cubics) that together form a region that is similar to the region being measured, then calculating the area for each of these shapes, and finally adding all of these small areas together
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Computer Numbering Formats
A computer number format is the internal representation of numeric values in digital computer and calculator hardware and software.[1] Normally, numeric values are stored as groupings of bits, named for the number of bits that compose them. The encoding between numerical values and bit patterns is chosen for convenience of the operation of the computer; the bit format used by the computer's instruction set generally requires conversion for external use such as printing and display. Different types of processors may have different internal representations of numerical values. Different conventions are used for integer and real numbers
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System Of Linear Equations
In mathematics, a system of linear equations (or linear system) is a collection of two or more linear equations involving the same set of variables.[1] For example, 3 x + 2 y − z = 1 2 x − 2 y + 4 z = − 2 − x + 1 2 y − z = 0 displaystyle begin alignedat 7 3x&&;+;&&2y&&;-;&&z&&;=;&&am
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Simplex Method
In mathematical optimization, Dantzig's simplex algorithm (or simplex method) is a popular algorithm for linear programming.[1] The name of the algorithm is derived from the concept of a simplex and was suggested by T. S. Motzkin.[2] Simplices are not actually used in the method, but one interpretation of it is that it operates on simplicial cones, and these become proper simplices with an additional constraint.[3][4][5][6] The simplicial cones in question are the corners (i.e., the neighborhoods of the vertices) of a geometric object called a polytope
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