Bisection method

In mathematics, the bisection method is a root-finding method that applies to any continuous function for which one knows two values with opposite signs. The method consists of repeatedly bisecting the interval defined by these values and then selecting the subinterval in which the function changes sign, and therefore must contain a root. It is a very simple and robust method, but it is also relatively slow. Because of this, it is often used to obtain a rough approximation to a solution which is then used as a starting point for more rapidly converging methods. The method is also called the interval halving method, the binary search method, or the dichotomy method. For polynomials, more elaborate methods exist for testing the existence of a root in an interval (Descartes' rule of signs, Sturm's theorem, Budan's theorem). They allow extending the bisection method into efficient algorithms for finding all real roots of a polynomial; see Real-root isolation. The method The

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (5)

Related publications

Related people

Related units

Related concepts (3)

Related concepts

Related courses (10)

Related courses

Related lectures (31)

Related lectures

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathema

Secant method

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought o

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 po

Analysis of Rainfall Data by Simple Good Sense: is Spatial Statistics Worth the Trouble ?

Reinhard Furrer

This paper discusses the use of simple good sense in the spatial prediction of rainfall measurements in Switzerland. The method consists of a forecast based on the values of the available observations combined with topographic knowledge of the Swiss territory. Comparison of our subjective estimates with the true measurements is completed and yields surprisingly good results.

1998

Structuration of micro-fluidic devices based on low temperature co-fired ceramic (LTCC) technology

Hansu Birol, Giancarlo Corradini, Yannick Fournier, Caroline Jacq, Thomas Maeder, Peter Ryser, Sigfrid Straessler

Smart packaging concept has been the driving force for the search of advanced technologies to produce multi-functional micro-scale devices for long years. In this sense, LTCC technology has been recently addressed as the suitable choice for a wide range of applications. In addition to its attractive characteristics for high-frequency applications those have been profited for a long time, it receives a growing attention for sensor applications in the recent years as well. This is due to the easy machinability of the LTCC tapes, which permits realization of complex structures such as membranes, channels, making it a suitable environment for micro-fluidic devices. These devices require utilization of supporting layers in order to prevent defects, often observed in forms of sagging, warpage or curling. The methods for elimination of these defects vary from passive precautions taken during lamination and firing to more elaborate methods such as use of sacrificial layers. The basic idea in the latter method is the preparation of a support, which can then be removed, leaving behind the desired structure. Among a number of alternatives, this paper focuses on and proposes the carbon-black sacrificial paste as an effective and simple method to fabricate membranes. Additionally determination of the open porosity elimination temperature in LTCC and effect of processing parameters on the fabricated structures, will be discussed. The methods of analysis will be TGA (thermo gravimetric analysis), dilatometer and SEM (scanning electron microscopy) analysis.

2005

A preconditioned low-rank CG method for parameter-dependent Lyapunov matrix equations

Daniel Kressner, Christine Tobler

This paper is concerned with the numerical solution of symmetric large-scale Lyapunov equations with low-rank right-hand sides and coefficient matrices depending on a parameter. Specifically, we consider the situation when the parameter dependence is sufficiently smooth, and the aim is to compute solutions for many different parameter samples. On the basis of existing results for Lyapunov equations and parameter-dependent linear systems, we prove that the tensor containing all solution samples typically allows for an excellent low multilinear rank approximation. Stacking all sampled equations into one huge linear system, this fact can be exploited by combining the preconditioned CG method with low-rank truncation. Our approach is flexible enough to allow for a variety of preconditioners based, for example, on the sign function iteration or the alternating direction implicit method. © 2013 John Wiley & Sons, Ltd.

Wiley-Blackwell2013

MATH-456: Numerical analysis and computational mathematics

The course provides an introduction to scientific computing. Several numerical methods are presented for the computer solution of mathematical problems arising in different applications. The software MATLAB is used to solve the problems and verify the theoretical properties of the numerical methods.

MATH-251(c): Numerical analysis

Le cours présente des méthodes numériques pour la résolution de problèmes mathématiques comme des systèmes d'équations linéaires ou non linéaires, approximation de fonctions, intégration et dérivation, équations différentielles.

MATH-251(a): Numerical analysis

This course presents numerical methods for the solution of mathematical problems such as systems of linear and non-linear equations, functions approximation, integration and differentiation and differential equations.