• Corpus ID: 6071578

Solving systems of linear interval equations using the "interval extended zero" method and multimedia extensions

  title={Solving systems of linear interval equations using the "interval extended zero" method and multimedia extensions},
  author={Mariusz Pilarek},
The aim of this paper is to present the implementa tion of the method for solving linear interval equations using the “interval exten d d zero” method and multimedia extensions. The “interval extended zero” method all ows us to reduce the undesirable excess width effect. Its efficiency was proven before and here we show that it can be used to perform fast calculations using multimedia extensio . Some numerical examples are used to illustrate the efficiency of our implementation i comparison… 

Tables from this paper

The Solution of Coupled Nonlinear Burgers' Equations Using Interval Finite-difference Method
In this paper an coupled Burgers’ equation is considered and then a method entitled interval finitedifference method is introduced to find the approximate interval solution of interval model in level
Is an interval the right result of arithmetic operations on intervals?
What conditions should be satisfied by the result of interval arithmetic operations to call it a “result”, how great its dimensionality is, how to perform arithmetic operations and solve equations are shown and examples illustrate the proposed method of interval computations.


Solving Systems of Interval Linear Equations with Use of Modified Interval Division Procedure
It is shown that a new method provides results close to the so-called maximal inner solution, which not only allows us to decrease the excess width effect, but makes it possible to avoid the inverted interval solutions too.
An iterative method for algebraic solution to interval equations
Abstract The algebraic solution to systems of linear equations involving an interval square matrix and an interval right-hand side vector in terms of interval arithmetic is discussed. The basic
On the Solution of Linear Algebraic Equations Involving Interval Coefficients
We discuss the solution to the interval algebraic systemA x b involving interval n n matrixA and interval vector b in directed interval arithmetic involving improper intervals We give some new
A new method for solving interval and fuzzy equations: Linear case
It is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number, and can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them.
Fuzzy Solution of Interval Nonlinear Equations
It is shown that opposite to the known methods, a new approach makes it possible to get both the positive and negative solutions of quadratic interval equation.
The Boost Interval Arithmetic Library
The design of the Boost interval arithmetic library is reported on, a C++ library designed to efficiently handle mathematical intervals in a generic way that is able to emulate almost any of the specialized libraries available for interval arithmetic.
Interval Arithmetic Using SSE-2
  • Branimir Lambov
  • Mathematics, Computer Science
    Reliable Implementation of Real Number Algorithms
  • 2006
The paper describes the ideas used to fit interval arithmetic to this set of instructions, shows a performance comparison with other freely available interval arithmetic packages, and discusses possible very simple hardware extensions that can significantly increase the performance of interval arithmetic.
Interval finite element method for beam structures
This paper presents a new method, the interval finite element method, to solve the uncertainty problems of the beam structures, where the beam characteristics are assumed to be represented as
Fast and Correct SIMD Algorithms for Interval Arithmetic
This work discusses these works, pointing out their achievements and shortcomings, and presents data storage and SIMD algorithms that are both correct and much faster than the fastest routines in standard interval libraries.
Interval Arithmetic on Multimedia Architectures
This paper shows how to implement interval arithmetic on multimedia architecture extensions with modest speed-up, and may be helpful in future design of hardware extensions for interval arithmetic.