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MINPACK
MINPACK is a library of Fortran subroutines for the solving of systems of nonlinear equations, or the least-squares minimization of the residual of a set of linear or nonlinear equations. MINPACK, along with other similar libraries such as LINPACK and EISPACK, originated from the Mathematics and Computer Science Division Software (MCS) of Argonne National Laboratory. Written by Jorge Moré, Burt Garbow, and Ken Hillstrom, MINPACK is free and designed to be highly portable, robust and reliable. The quality of its implementation of the Levenberg–Marquardt algorithm is attested by Dennis and Schnabel. Five algorithmic paths each include a core subroutine and a driver routine. The algorithms proceed either from an analytic specification of the Jacobian matrix In vector calculus, the Jacobian matrix (, ) of a vector-valued function of several variables is the matrix of all its first-order partial derivatives. If this matrix is square, that is, if the number of variables equa ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
EISPACK
EISPACK is a software library for numerical computation of eigenvalues and eigenvectors of matrices, written in FORTRAN. It contains subroutines for calculating the eigenvalues of nine classes of matrices: complex general, complex Hermitian, real general, real symmetric, real symmetric banded, real symmetric tridiagonal, special real tridiagonal, generalized real, and generalized real symmetric matrices. In addition, it includes subroutines to perform a singular value decomposition. Originally written around 1972–1973, EISPACK, like LINPACK and MINPACK, originated from Argonne National Laboratory, has always been free, and aims to be portable, robust and reliable. The library drew heavily on algorithms developed by James Wilkinson, which were originally implemented in ALGOL ALGOL (; short for "Algorithmic Language") is a family of imperative computer programming languages originally developed in 1958. ALGOL heavily influenced many other languages and was the standard m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nonlinear System
In mathematics and science, a nonlinear system (or a non-linear system) is a system in which the change of the output is not proportional to the change of the input. Nonlinear problems are of interest to engineers, biologists, physicists, mathematicians, and many other scientists since most systems are inherently nonlinear in nature. Nonlinear dynamical systems, describing changes in variables over time, may appear chaotic, unpredictable, or counterintuitive, contrasting with much simpler linear systems. Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equations, which is a set of simultaneous equations in which the unknowns (or the unknown functions in the case of differential equations) appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one. In other words, in a nonlinear system of equations, the equation(s) to be solved cannot be written as a lin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Least-squares
The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The method is widely used in areas such as regression analysis, curve fitting and data modeling. The least squares method can be categorized into linear and nonlinear forms, depending on the relationship between the model parameters and the observed data. The method was first proposed by Adrien-Marie Legendre in 1805 and further developed by Carl Friedrich Gauss. History Founding The method of least squares grew out of the fields of astronomy and geodesy, as scientists and mathematicians sought to provide solutions to the challenges of navigating the Earth's oceans during the Age of Discovery. The accurate description of the behavior of celestial bodies was the key to enabling ships to sail in open seas, where sailors could no longer rely on la ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 variable (math), variables. For example, : \begin 3x+2y-z=1\\ 2x-2y+4z=-2\\ -x+\fracy-z=0 \end is a system of three equations in the three variables . A ''Solution (mathematics), solution'' to a linear system is an assignment of values to the variables such that all the equations are simultaneously satisfied. In the example above, a solution is given by the Tuple, ordered triple (x,y,z)=(1,-2,-2), since it makes all three equations valid. Linear systems are a fundamental part of linear algebra, a subject used in most modern mathematics. Computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A Nonlinear system, system of non-linear equations can often be Approximation, approximated by a linear system (see linea ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
LINPACK
LINPACK is a software library for performing numerical linear algebra on digital computers. It was written in Fortran by Jack Dongarra, Jim Bunch, Cleve Moler, and Gilbert Stewart, and was intended for use on supercomputers in the 1970s and early 1980s. It has been largely superseded by LAPACK, which runs more efficiently on modern architectures. LINPACK makes use of the BLAS (Basic Linear Algebra Subprograms) libraries for performing basic vector and matrix operations. The LINPACK benchmarks appeared initially as part of the LINPACK user's manual. The parallel LINPACK benchmark implementation called HPL (High Performance Linpack) is used to benchmark and rank supercomputers for the TOP500 The TOP500 project ranks and details the 500 most powerful non-distributed computing, distributed computer systems in the world. The project was started in 1993 and publishes an updated list of the supercomputers twice a year. The first of these ... list. World's most powerful com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Argonne National Laboratory
Argonne National Laboratory is a Federally funded research and development centers, federally funded research and development center in Lemont, Illinois, Lemont, Illinois, United States. Founded in 1946, the laboratory is owned by the United States Department of Energy and administered by UChicago Argonne LLC of the University of Chicago. The facility is the largest national laboratory in the Midwestern United States, Midwest. Argonne had its beginnings in the Metallurgical Laboratory of the University of Chicago, formed in part to carry out Enrico Fermi's work on nuclear reactors for the Manhattan Project during World War II. After the war, it was designated as the first national laboratory in the United States on July 1, 1946. In its first decades, the laboratory was a hub for peaceful use of nuclear physics; nearly all operating commercial nuclear power plants around the world have roots in Argonne research. More than 1,000 scientists conduct research at the laboratory, in the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jorge J
Jorge is the Spanish and Portuguese form of the given name George. While spelled alike, this name is pronounced very differently in each of the two languages: Spanish ; Portuguese . It is derived from the Greek name Γεώργιος (''Georgios'') via Latin ''Georgius''; the former is derived from (''georgos''), meaning "farmer" or "earth-worker". The Latin form ''Georgius'' had been rarely given in Western Christendom since at least the 6th century. The popularity of the name however develops from around the 12th century, in Occitan in the form '' Jordi'', and it becomes popular at European courts after the publication of the ''Golden Legend'' in the 1260s. The West Iberian form ''Jorge'' is on record in Portugal as the name of Jorge de Lencastre, Duke of Coimbra (1481–1550). List of people with the given name Jorge * Jorge (footballer, born 1939), Brazilian footballer * Jorge (footballer, born 1946), Brazilian footballer * Jorge (Brazilian singer), Brazilian musician ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Burt Garbow
Burt is a given name and also a shortened form of other names, such as Burton and Herbert, or a place name. Burt may refer to: People * Burt Alvord (1866–after 1910), American Old West lawman and outlaw * Burt Aull (1871–1947), American football player *Burt Bacharach (1928–2023), American composer, music producer and pianist *Burt Balaban (1922–1965), American film producer and director *Burt Bales (1916–1969), American jazz stride pianist * Burt Brown Barker (1873–1960), American lawyer and administrator * Burt Baskin (1913–1967), American co-founder of the Baskin-Robbins ice cream parlor chain * Burt Blague (born 1975), Russian circus performer, comedian and director * Burt Blanca (born 1944), Belgian rock and roll musician * Burt Boutin, American professional poker player * Burt Boyar (1927–2018), American columnist, voice actor and author * Burt Brent, American reconstructive plastic surgeon *Burt Brinckerhoff (born 1936), American actor, director and producer ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ken Hillstrom
Ken or KEN may refer to: Entertainment * ''Ken'' (album), a 2017 album by Canadian indie rock band Destroyer * ''Ken'' (film), a 1965 Japanese film * ''Ken'' (magazine), a large-format political magazine * Ken Masters, a main character in the ''Street Fighter'' franchise People * Ken (given name), a list of people named Ken * Ken (musician) (born 1968), guitarist of the Japanese rock band L'Arc-en-Ciel * Ken (South Korean singer) (born 1992), stage name of Lee Jae-hwan of the South Korean boy group VIXX * Felip (singer), member of SB19 who goes by stage name Ken Other uses * Kèn, a musical instrument from Vietnam * Ken (doll), a product by Mattel * ''Ken'' (unit) (間), a Japanese unit of measurement and proportion * Ken River, a river in the Bundelkhand region, India * ''Ken'' sword (剣), a Japanese sword * Kensington railway station, Melbourne * Komisja Edukacji Narodowej, Polish National Board of Education * ''Ken'' (県), meaning "prefecture" in Japanese; see Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Software Portability
Software consists of computer programs that instruct the execution of a computer. Software also includes design documents and specifications. The history of software is closely tied to the development of digital computers in the mid-20th century. Early programs were written in the machine language specific to the hardware. The introduction of high-level programming languages in 1958 allowed for more human-readable instructions, making software development easier and more portable across different computer architectures. Software in a programming language is run through a compiler or interpreter to execute on the architecture's hardware. Over time, software has become complex, owing to developments in networking, operating systems, and databases. Software can generally be categorized into two main types: # operating systems, which manage hardware resources and provide services for applications # application software, which performs specific tasks for users The r ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Levenberg–Marquardt Algorithm
In mathematics and computing, the Levenberg–Marquardt algorithm (LMA or just LM), also known as the damped least-squares (DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the method of gradient descent. The LMA is more robust than the GNA, which means that in many cases it finds a solution even if it starts very far off the final minimum. For well-behaved functions and reasonable starting parameters, the LMA tends to be slower than the GNA. LMA can also be viewed as Gauss–Newton using a trust region approach. The algorithm was first published in 1944 by Kenneth Levenberg, while working at the Frankford Army Arsenal. It was rediscovered in 1963 by Donald Marquardt, who worked as a statistician at DuPont, and independently by Girard, Wynne and Morrison. The LMA is used in many software applications for solv ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
