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MPSolve
MPSolve (Multiprecision Polynomial Solver) is a package for the Root-finding algorithm, approximation of the roots of a polynomial, univariate polynomial. It uses the Aberth method, combined with a careful use of multiprecision. "Mpsolve takes advantage of Sparse matrix, sparsity, and has special hooking, hooks for polynomials that can be evaluated efficiently by straight-line programs" Implementation The program is written mostly in C (programming language), ANSI C and makes use of the GNU Multi-Precision Library. It uses a command-line interface (CLI) and, starting from version 3.1.0 has also a Graphical user interface, GUI and interfaces for MATLAB and GNU Octave, GNU/Octave. Usage The executable program of the package is called mpsolve. It can be execution (computers), run from command line in terminal emulator, console. The executable file for the graphical user interface is called xmpsolve, and the MATLAB and Octave functions are called mps_roots. They behave similarly t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Root-finding Algorithm
In mathematics and computing, a root-finding algorithm is an algorithm for finding zeros, also called "roots", of continuous functions. A zero of a function , from the real numbers to real numbers or from the complex numbers to the complex numbers, is a number such that . As, generally, the zeros of a function cannot be computed exactly nor expressed in closed form, root-finding algorithms provide approximations to zeros, expressed either as floating-point numbers or as small isolating intervals, or disks for complex roots (an interval or disk output being equivalent to an approximate output together with an error bound). Solving an equation is the same as finding the roots of the function . Thus root-finding algorithms allow solving any equation defined by continuous functions. However, most root-finding algorithms do not guarantee that they will find all the roots; in particular, if such an algorithm does not find any root, that does not mean that no root exists. Most nume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aberth Method
The Aberth method, or Aberth–Ehrlich method or Ehrlich–Aberth method, named after Oliver Aberth and Louis W. Ehrlich, is a root-finding algorithm developed in 1967 for simultaneous approximation of all the roots of a univariate polynomial. This method converges cubically, an improvement over the Durand–Kerner method, another algorithm for approximating all roots at once, which converges quadratically. (However, both algorithms converge linearly at multiple zeros.) This method is used in MPSolve, which is the reference software for approximating all roots of a polynomial to an arbitrary precision. Description Let p(x)=p_nx^n+p_x^+\cdots+p_1x+p_0 be a univariate polynomial of degree ''n'' with real or complex coefficients. Then there exist complex numbers z^*_1,\,z^*_2,\dots,z^*_n, the roots of ''p(x)'', that give the factorization: :p(x)=p_n\cdot(x-z^*_1)\cdot(x-z^*_2)\cdots(x-z^*_n). Although those numbers are unknown, upper and lower bounds for their absolute values ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Polynomial Root-finding Algorithms
Finding polynomial roots is a long-standing problem that has been the object of much research throughout history. A testament to this is that up until the 19th century, algebra meant essentially theory of polynomial equations. Principles Finding the root of a linear polynomial (degree one) is easy and needs only one division: the general equation ax + b = 0 has solution x = -b/a. For quadratic polynomials (degree two), the quadratic formula produces a solution, but its numerical evaluation may require some care for ensuring numerical stability. For degrees three and four, there are closed-form solutions in terms of radicals, which are generally not convenient for numerical evaluation, as being too complicated and involving the computation of several th roots whose computation is not easier than the direct computation of the roots of the polynomial (for example the expression of the real roots of a cubic polynomial may involve non-real cube roots). For polynomials of degree fi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language)
C (''pronounced like the letter c'') is a General-purpose language, general-purpose computer programming language. It was created in the 1970s by Dennis Ritchie, and remains very widely used and influential. By design, C's features cleanly reflect the capabilities of the targeted CPUs. It has found lasting use in operating systems, device drivers, protocol stacks, though decreasingly for application software. C is commonly used on computer architectures that range from the largest supercomputers to the smallest microcontrollers and embedded systems. A successor to the programming language B (programming language), B, C was originally developed at Bell Labs by Ritchie between 1972 and 1973 to construct utilities running on Unix. It was applied to re-implementing the kernel of the Unix operating system. During the 1980s, C gradually gained popularity. It has become one of the measuring programming language popularity, most widely used programming languages, with C compilers avail ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Execution (computers)
Execution in computer and software engineering is the process by which a computer or virtual machine reads and acts on the instructions of a computer program. Each instruction of a program is a description of a particular action which must be carried out, in order for a specific problem to be solved. Execution involves repeatedly following a ' fetch–decode–execute' cycle for each instruction done by control unit. As the executing machine follows the instructions, specific effects are produced in accordance with the semantics of those instructions. Programs for a computer may be executed in a batch process without human interaction or a user may type commands in an interactive session of an interpreter. In this case, the "commands" are simply program instructions, whose execution is chained together. The term run is used almost synonymously. A related meaning of both "to run" and "to execute" refers to the specific action of a user starting (or ''launching'' or ''invokin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Software Programmed In C
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media personal ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Mathematics Software
Free may refer to: Concept * Freedom, having the ability to do something, without having to obey anyone/anything * Freethought, a position that beliefs should be formed only on the basis of logic, reason, and empiricism * Emancipate, to procure political rights, as for a disenfranchised group * Free will, control exercised by rational agents over their actions and decisions * Free of charge, also known as gratis. See Gratis vs libre. Computing * Free (programming), a function that releases dynamically allocated memory for reuse * Free format, a file format which can be used without restrictions * Free software, software usable and distributable with few restrictions and no payment * Freeware, a broader class of software available at no cost Mathematics * Free object ** Free abelian group ** Free algebra ** Free group ** Free module ** Free semigroup * Free variable People * Free (surname) * Free (rapper) (born 1968), or Free Marie, American rapper and media personality ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
C (programming Language) Software
C, or c, is the third letter in the Latin alphabet, used in the modern English alphabet, the alphabets of other western European languages and others worldwide. Its name in English is ''cee'' (pronounced ), plural ''cees''. History "C" comes from the same letter as "G". The Semites named it gimel. The sign is possibly adapted from an Egyptian hieroglyph for a staff sling, which may have been the meaning of the name ''gimel''. Another possibility is that it depicted a camel, the Semitic name for which was ''gamal''. Barry B. Powell, a specialist in the history of writing, states "It is hard to imagine how gimel = "camel" can be derived from the picture of a camel (it may show his hump, or his head and neck!)". In the Etruscan language, plosive consonants had no contrastive voicing, so the Greek ' Γ' (Gamma) was adopted into the Etruscan alphabet to represent . Already in the Western Greek alphabet, Gamma first took a '' form in Early Etruscan, then '' in Classical Etru ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gnuplot
gnuplot is a command-line and GUI program that can generate two- and three-dimensional plots of functions, data, and data fits. The program runs on all major computers and operating systems (Linux, Unix, Microsoft Windows, macOS, FreeDOS, and many others). Originally released in 1986, its listed authors are Thomas Williams, Colin Kelley, Russell Lang, Dave Kotz, John Campbell, Gershon Elber, Alexander Woo "and many others." Despite its name, this software is not part of the GNU Project. Features gnuplot can produce output directly on screen, or in many formats of graphics files, including Portable Network Graphics (PNG), Encapsulated PostScript (EPS), Scalable Vector Graphics (SVG), JPEG and many others. It is also capable of producing LaTeX code that can be included directly in LaTeX documents, making use of LaTeX's fonts and powerful formula notation abilities. The program can be used both interactively and in batch mode using scripts. gnuplot can read data in multiple ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Filename Extension
A filename extension, file name extension or file extension is a suffix to the name of a computer file (e.g., .txt, .docx, .md). The extension indicates a characteristic of the file contents or its intended use. A filename extension is typically delimited from the rest of the filename with a full stop (period), but in some systems it is separated with spaces. Other extension formats include dashes and/or underscores on early versions of Linux and some versions of IBM AIX. Some file systems implement filename extensions as a feature of the file system itself and may limit the length and format of the extension, while others treat filename extensions as part of the filename without special distinction. Usage Filename extensions may be considered a type of metadata. They are commonly used to imply information about the way data might be stored in the file. The exact definition, giving the criteria for deciding what part of the file name is its extension, belongs to the rules of th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Terminal Emulator
A terminal emulator, or terminal application, is a computer program that emulates a video terminal within some other display architecture. Though typically synonymous with a shell or text terminal, the term ''terminal'' covers all remote terminals, including graphical interfaces. A terminal emulator inside a graphical user interface is often called a terminal window. A terminal window allows the user access to a text terminal and all its applications such as command-line interfaces (CLI) and text user interface (TUI) applications. These may be running either on the same machine or on a different one via telnet, ssh, dial-up, or over a direct serial connection. On Unix-like operating systems, it is common to have one or more terminal windows connected to the local machine. Terminals usually support a set of escape sequences for controlling color, cursor position, etc. Examples include the family of terminal control sequence standards known as ECMA-48, ANSI X3.64 or ISO/IEC 6 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
