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Math Library
In computer science, a math library (or maths library) is a component of a programming language's standard library containing functions (or subroutines) for the most common mathematical functions, such as trigonometry and exponentiation. Bit-twiddling and control functionalities related to floating point numbers may also be included (such as in C). Examples include: * the C standard library math functions, * Java maths library * 'Prelude.Math' in haskell. In some languages (such as haskell) parts of the standard library (including maths) are imported by default. More advanced functionality such as linear algebra is usually provided in 3rd party libraries, such as a linear algebra library or vector maths library. Implementation outline Basic operations In a math library, it is frequently useful to use type punning to interpret a floating-point number as an unsigned integer of the same size. This allows for faster inspection of certain numeral properties (positive or not) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Computer Science
Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to practical disciplines (including the design and implementation of hardware and software). Computer science is generally considered an area of academic research and distinct from computer programming. Algorithms and data structures are central to computer science. The theory of computation concerns abstract models of computation and general classes of problems that can be solved using them. The fields of cryptography and computer security involve studying the means for secure communication and for preventing security vulnerabilities. Computer graphics and computational geometry address the generation of images. Programming language theory considers different ways to describe computational processes, and database theory concerns the management of repositories ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Vector Maths Library
This is a glossary of terms relating to computer graphics. For more general computer hardware terms, see glossary of computer hardware terms. 0–9 A B C D E F G H I K L M N O P Q R S T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intrinsic Function
In computer software, in compiler theory, an intrinsic function (or built-in function) is a function (subroutine) available for use in a given programming language whose implementation is handled specially by the compiler. Typically, it may substitute a sequence of automatically generated instructions for the original function call, similar to an inline function. Unlike an inline function, the compiler has an intimate knowledge of an intrinsic function and can thus better integrate and optimize it for a given situation. Compilers that implement intrinsic functions generally enable them only when a program requests optimization, otherwise falling back to a default implementation provided by the language runtime system (environment). Intrinsic functions are often used to explicitly implement vectorization and parallelization in languages which do not address such constructs. Some application programming interfaces (API), for example, AltiVec and OpenMP, use intrinsic function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Horner's Method
In mathematics and computer science, Horner's method (or Horner's scheme) is an algorithm for polynomial evaluation. Although named after William George Horner, this method is much older, as it has been attributed to Joseph-Louis Lagrange by Horner himself, and can be traced back many hundreds of years to Chinese and Persian mathematicians. After the introduction of computers, this algorithm became fundamental for computing efficiently with polynomials. The algorithm is based on Horner's rule: :\begin a_0 &+ a_1x + a_2x^2 + a_3x^3 + \cdots + a_nx^n \\ &= a_0 + x \bigg(a_1 + x \Big(a_2 + x \big(a_3 + \cdots + x(a_ + x \, a_n) \cdots \big) \Big) \bigg). \end This allows the evaluation of a polynomial of degree with only n multiplications and n additions. This is optimal, since there are polynomials of degree that cannot be evaluated with fewer arithmetic operations. Alternatively, Horner's method also refers to a method for approximating the roots of polynomials, described by H ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Remez Algorithm
The Remez algorithm or Remez exchange algorithm, published by Evgeny Yakovlevich Remez in 1934, is an iterative algorithm used to find simple approximations to functions, specifically, approximations by functions in a Chebyshev space that are the best in the uniform norm ''L''∞ sense. It is sometimes referred to as Remes algorithm or Reme algorithm. A typical example of a Chebyshev space is the subspace of Chebyshev polynomials of order ''n'' in the space of real continuous functions on an interval, ''C'' 'a'', ''b'' The polynomial of best approximation within a given subspace is defined to be the one that minimizes the maximum absolute difference between the polynomial and the function. In this case, the form of the solution is precised by the equioscillation theorem. Procedure The Remez algorithm starts with the function f to be approximated and a set X of n + 2 sample points x_1, x_2, ...,x_ in the approximation interval, usually the extrema of Chebyshev polynomial line ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chebyshev Polynomial
The Chebyshev polynomials are two sequences of polynomials related to the cosine and sine functions, notated as T_n(x) and U_n(x). They can be defined in several equivalent ways, one of which starts with trigonometric functions: The Chebyshev polynomials of the first kind T_n are defined by : T_n(\cos \theta) = \cos(n\theta). Similarly, the Chebyshev polynomials of the second kind U_n are defined by : U_n(\cos \theta) \sin \theta = \sin\big((n + 1)\theta\big). That these expressions define polynomials in \cos\theta may not be obvious at first sight, but follows by rewriting \cos(n\theta) and \sin\big((n+1)\theta\big) using de Moivre's formula or by using the angle sum formulas for \cos and \sin repeatedly. For example, the double angle formulas, which follow directly from the angle sum formulas, may be used to obtain T_2(\cos\theta)=\cos(2\theta)=2\cos^2\theta-1 and U_1(\cos\theta)\sin\theta=\sin(2\theta)=2\cos\theta\sin\theta, which are respectively a polynomial in \cos\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Taylor Polynomial
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first terms of a Taylor series is a polynomial of degree that is called the th Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Fit
In statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable ''x'' and the dependent variable ''y'' is modelled as an ''n''th degree polynomial in ''x''. Polynomial regression fits a nonlinear relationship between the value of ''x'' and the corresponding conditional mean of ''y'', denoted E(''y'' , ''x''). Although ''polynomial regression'' fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function E(''y'' , ''x'') is linear in the unknown parameters that are estimated from the data. For this reason, polynomial regression is considered to be a special case of multiple linear regression. The explanatory (independent) variables resulting from the polynomial expansion of the "baseline" variables are known as higher-degree terms. Such variables are also used in classification settings. History Polynomial regression models are us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Transcendental Function
In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation, in contrast to an algebraic function. In other words, a transcendental function "transcends" algebra in that it cannot be expressed algebraically. Examples of transcendental functions include the exponential function, the logarithm, and the trigonometric functions. Definition Formally, an analytic function ''f''(''z'') of one real or complex variable ''z'' is transcendental if it is algebraically independent of that variable. This can be extended to functions of several variables. History The transcendental functions sine and cosine were tabulated from physical measurements in antiquity, as evidenced in Greece (Hipparchus) and India ( jya and koti-jya). In describing Ptolemy's table of chords, an equivalent to a table of sines, Olaf Pedersen wrote: A revolutionary understanding of these circular functions occurred in the 17th century and was explicated by Leonhar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bit Twiddling
Bit manipulation is the act of algorithmically manipulating bits or other pieces of data shorter than a word. Computer programming tasks that require bit manipulation include low-level device control, error detection and correction algorithms, data compression, encryption algorithms, and optimization. For most other tasks, modern programming languages allow the programmer to work directly with abstractions instead of bits that represent those abstractions. Source code that does bit manipulation makes use of the bitwise operations: AND, OR, XOR, NOT, and possibly other operations analogous to the boolean operators; there are also bit shifts and operations to count ones and zeros, find high and low one or zero, set, reset and test bits, extract and insert fields, mask and zero fields, gather and scatter bits to and from specified bit positions or fields. Integer arithmetic operators can also effect bit-operations in conjunction with the other operators. Bit manipulation, in som ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Type Punning
In computer science, a type punning is any programming technique that subverts or circumvents the type system of a programming language in order to achieve an effect that would be difficult or impossible to achieve within the bounds of the formal language. In C and C++, constructs such as pointer type conversion and union — C++ adds reference type conversion and reinterpret_cast to this list — are provided in order to permit many kinds of type punning, although some kinds are not actually supported by the standard language. In the Pascal programming language, the use of records with variants may be used to treat a particular data type in more than one manner, or in a manner not normally permitted. Sockets example One classic example of type punning is found in the Berkeley sockets interface. The function to bind an opened but uninitialized socket to an IP address is declared as follows: int bind(int sockfd, struct sockaddr *my_addr, socklen_t addrlen); The bind ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Algebra Library
The following tables provide a comparison of linear algebra software libraries, either specialized or general purpose libraries with significant linear algebra coverage. Dense linear algebra General information Matrix types and operations Matrix types (special types like bidiagonal/tridiagonal are not listed): * ''Real'' – general (nonsymmetric) real * ''Complex'' – general (nonsymmetric) complex * ''SPD'' – symmetric positive definite (real) * ''HPD'' – Hermitian positive definite (complex) * ''SY'' – symmetric (real) * ''HE'' – Hermitian (complex) * ''BND'' – band Operations: * ''TF'' – triangular factorizations (LU, Cholesky) * ''OF'' – orthogonal factorizations (QR, QL, generalized factorizations) * ''EVP'' – eigenvalue problems * ''SVD'' – singular value decomposition In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix. It generalizes the eigendecomposition of a square normal matrix w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
