MPSolve (Multiprecision Polynomial Solver) is a package for the approximation of the roots of a

univariate polynomial In mathematics, a polynomial is an expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication, and positive-integer powers of variables. An example ...

. It uses the

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 ...

, combined with a careful use of multiprecision. "Mpsolve takes advantage of

sparsity In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse b ...

, and has special hooks for polynomials that can be evaluated efficiently by straight-line programs"

Implementation

The program is written mostly in ANSI C and makes use of the

GNU Multi-Precision Library GNU Multiple Precision Arithmetic Library (GMP) is a free library for arbitrary-precision arithmetic, operating on signed integers, rational numbers, and floating-point numbers. There are no practical limits to the precision except the ones imp ...

. It uses a

command-line interface A command-line interpreter or command-line processor uses a command-line interface (CLI) to receive commands from a user in the form of lines of text. This provides a means of setting parameters for the environment, invoking executables and pro ...

(CLI) and, starting from version 3.1.0 has also a

GUI The GUI ( "UI" by itself is still usually pronounced . or ), graphical user interface, is a form of user interface that allows users to interact with electronic devices through graphical icons and audio indicator such as primary notation, inste ...

and interfaces for

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 ...

and GNU/Octave.

Usage

The executable program of the package is called mpsolve. It can be

run Run(s) or RUN may refer to: Places * Run (island), one of the Banda Islands in Indonesia * Run (stream), a stream in the Dutch province of North Brabant People * Run (rapper), Joseph Simmons, now known as "Reverend Run", from the hip-hop group ...

from command line in 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 to the function roots that is already included in these software packages.

Output

Typically output will be on the screen. It may also be saved as a text file (with res

extension Extension, extend or extended may refer to: Mathematics Logic or set theory * Axiom of extensionality * Extensible cardinal * Extension (model theory) * Extension (predicate logic), the set of tuples of values that satisfy the predicate * E ...

) and plotted in

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, an ...

. Direct plotting in

is also supported on Unix systems.

References

External links

{{Wikibooks, MPSolve
Home page
C (programming language) software Free mathematics software Free software programmed in C Numerical software Software using the GPL license

Implementation

Usage

Output

See also

References

External links