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Sobol Sequence
Sobol’ sequences (also called LPτ sequences or (''t'', ''s'') sequences in base 2) are a type of quasi-random low-discrepancy sequence. They were first introduced by the Russian mathematician Ilya M. Sobol’ (Илья Меерович Соболь) in 1967.Sobol’, I.M. (1967), "Distribution of points in a cube and approximate evaluation of integrals". ''Zh. Vych. Mat. Mat. Fiz.'' 7: 784–802 (in Russian); ''U.S.S.R Comput. Maths. Math. Phys.'' 7: 86–112 (in English). These sequences use a base of two to form successively finer uniform partitions of the unit interval and then reorder the coordinates in each dimension. Good distributions in the ''s''-dimensional unit hypercube Let be the -dimensional unit hypercube, and a real integrable function over . The original motivation of Sobol’ was to construct a sequence in so that \lim_ \frac \sum_^n f(x_i) = \int_ f and the convergence be as fast as possible. It is more or less clear that for the sum to c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Low-discrepancy Sequence
In mathematics, a low-discrepancy sequence is a sequence with the property that for all values of N, its subsequence x_1, \ldots, x_N has a low discrepancy of a sequence, discrepancy. Roughly speaking, the discrepancy of a sequence is low if the proportion of points in the sequence falling into an arbitrary set ''B'' is close to proportional to the Measure (mathematics), measure of ''B'', as would happen on average (but not for particular samples) in the case of an equidistributed sequence. Specific definitions of discrepancy differ regarding the choice of ''B'' (hyperspheres, Hypercube, hypercubes, etc.) and how the discrepancy for every B is computed (usually normalized) and combined (usually by taking the worst value). Low-discrepancy sequences are also called quasirandom sequences, due to their common use as a replacement of uniformly distributed random sequence, random numbers. The "quasi" modifier is used to denote more clearly that the values of a low-discrepancy sequence ar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
John Wiley And Sons
John Wiley & Sons, Inc., commonly known as Wiley (), is an American multinational publishing company that focuses on academic publishing and instructional materials. The company was founded in 1807 and produces books, journals, and encyclopedias, in print and electronically, as well as online products and services, training materials, and educational materials for undergraduate, graduate, and continuing education students. History The company was established in 1807 when Charles Wiley opened a print shop in Manhattan. The company was the publisher of 19th century American literary figures like James Fenimore Cooper, Washington Irving, Herman Melville, and Edgar Allan Poe, as well as of legal, religious, and other non-fiction titles. The firm took its current name in 1865. Wiley later shifted its focus to scientific, technical, and engineering subject areas, abandoning its literary interests. Wiley's son John (born in Flatbush, New York, October 4, 1808; died in East ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
NAG Numerical Libraries
The NAG Numerical Library is a commercial software product developed and sold by The Numerical Algorithms Group Ltd. It is a software library of numerical-analysis routines, containing more than 1,900 mathematical and statistical algorithms. Areas covered by the library include linear algebra, optimization, quadrature, the solution of ordinary and partial differential equations, regression analysis, and time series analysis. Users of the NAG Library call its routines from within their applications to incorporate its mathematical or statistical functionality and to solve numerical problems - for example, finding the minimum or maximum of a function, fitting a curve or surface to data, or solving a differential equation. The NAG Library can be accessed from a variety of programming languages and environments such as C/ C++, Fortran, Python, Active Directory (AD), MATLAB, Java, and .NET. The main supported systems are currently Windows, Linux and macOS running on x86-64 arc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Python (programming Language)
Python is a high-level programming language, high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. Python is type system#DYNAMIC, dynamically type-checked and garbage collection (computer science), garbage-collected. It supports multiple programming paradigms, including structured programming, structured (particularly procedural programming, procedural), object-oriented and functional programming. It is often described as a "batteries included" language due to its comprehensive standard library. Guido van Rossum began working on Python in the late 1980s as a successor to the ABC (programming language), ABC programming language, and he first released it in 1991 as Python 0.9.0. Python 2.0 was released in 2000. Python 3.0, released in 2008, was a major revision not completely backward-compatible with earlier versions. Python 2.7.18, released in 2020, was the last release of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Matlab
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Julia (programming Language)
Julia is a high-level programming language, high-level, general-purpose programming language, general-purpose dynamic programming language, dynamic programming language, designed to be fast and productive, for e.g. data science, artificial intelligence, machine learning, modeling and simulation, most commonly used for numerical analysis and computational science. Distinctive aspects of Julia's design include a type system with parametric polymorphism and the use of multiple dispatch as a core programming paradigm, a default just-in-time compilation, just-in-time (JIT) compiler (with support for ahead-of-time compilation) and an tracing garbage collection, efficient (multi-threaded) garbage collection implementation. Notably Julia does not support classes with encapsulated methods and instead it relies on structs with generic methods/functions not tied to them. By default, Julia is run similarly to scripting languages, using its runtime, and allows for read–eval–print loop, i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free And Open-source Software
Free and open-source software (FOSS) is software available under a license that grants users the right to use, modify, and distribute the software modified or not to everyone free of charge. FOSS is an inclusive umbrella term encompassing free software and open-source software. The rights guaranteed by FOSS originate from the "Four Essential Freedoms" of '' The Free Software Definition'' and the criteria of '' The Open Source Definition''. All FOSS can have publicly available source code, but not all source-available software is FOSS. FOSS is the opposite of proprietary software, which is licensed restrictively or has undisclosed source code. The historical precursor to FOSS was the hobbyist and academic public domain software ecosystem of the 1960s to 1980s. Free and open-source operating systems such as Linux distributions and descendants of BSD are widely used, powering millions of servers, desktops, smartphones, and other devices. Free-software licenses and open-so ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Recipes
''Numerical Recipes'' is the generic title of a series of books on algorithm In mathematics and computer science, an algorithm () is a finite sequence of Rigour#Mathematics, mathematically rigorous instructions, typically used to solve a class of specific Computational problem, problems or to perform a computation. Algo ...s and numerical analysis by William H. Press, Saul A. Teukolsky, William T. Vetterling and Brian P. Flannery. In various editions, the books have been in print since 1986. The most recent edition was published in 2007. Overview The ''Numerical Recipes'' books cover a range of topics that include both classical numerical analysis (interpolation, Numerical integration, integration, linear algebra, differential equations, and so on), signal processing (Fast Fourier transform, Fourier methods, Digital filter, filtering), statistical treatment of data, and a few topics in machine learning (hidden Markov model, support vector machines). The writing style is acc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods In Finance
Monte Carlo methods are used in corporate finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining the distribution of their value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase. Monte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his ''Harvard Business Review'' article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal ''Journal of Financial Economics'' paper. This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called "quasi-random" methods such as the use of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ilya M
Ilya, Iliya, Ilia, Ilja, Ilija, or Illia ( , or ; ; ) is the East Slavic form of the male Hebrew name Eliyahu (Eliahu), meaning "My God is Yahu/Jah." It comes from the Byzantine Greek pronunciation of the vocative (Ilía) of the Greek Elias (Ηλίας, Ilías). It is pronounced with stress on the second syllable. The diminutive form is Iliusha or Iliushen'ka. The Russian patronymic for a son of Ilya is " Ilyich", and a daughter is "Ilyinichna". People with the name Real people *Ilya (Archbishop of Novgorod), 12th-century Russian Orthodox cleric and saint *Ilya Ivanovitch Alekseyev (1772–1830), commander of the Russian Imperial Army *Ilya Borok (born 1993), Russian jiujitsu fighter *Ilya Bryzgalov (born 1980), Russian ice hockey goalie * Ilya Dzhirkvelov (1927–2006), author and KGB defector *Ilya Ehrenburg (1891–1967), Russian writer and Soviet cultural ambassador *Ilya Frank (1908–1990), Russian physicist *Ilya Glazunov (1930–2017), Russian painter *Ilya Gringolts ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Peter Jaeckel
Peter Jaeckel (Peter Jäckel) is a mathematician, finance professor and market practitioner. He is the managing director of OTC Analytics. He also teaches at the Certificate of Quantitative Finance (CQF, FitchLearning) programme and at Oxford University. Previously, he was a managing director (Deputy Head of Quantitative Research) at VTB Europe (Frankfurt) and VTB Capital (London). Before that, Global Head of Credit, Hybrid, Inflation, and Commodity Derivative Analytics at ABN Amro, and also held several positions at Nikko Securities, NatWest (Royal Bank of Scotland group), and Commerzbank Securities' product development group. He is the author of the bestselling ''Monte Carlo methods in finance'' (John Wiley and Sons, ). In mathematics, he has made important contributions to the field of Sobol sequences; while in Mathematical Finance, he has been influential in the development of Monte Carlo methods in finance, and has also contributed, to the LIBOR market model, and volatility m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
