
	Where results make sense

Topic: Bisection

In the News (Tue 2 Dec 08)

Damian Green

Sumner Redstone

Crimson Tide

Tommy Tuberville

Bill Clinton

Wayne Rooney

Vilasrao Deshmukh

Wake Forest

Grand Slam

Oklahoma State

	Bisection
		In classical geometry, the bisection is a simple ruler-and-compass construction, whose possibility depends on the ability to draw circles of equivalent radius and different centers.
		The segment is bisected by drawing intersecting circles of equal radius, whose centers are the endpoints of the segment.
		To bisect an angle, one draws a circle whose center is the vertex.
	www.brainyencyclopedia.com /encyclopedia/b/bi/bisection.html (397 words)

	Bisection method - Wikipedia, the free encyclopedia
		In mathematics, the bisection method is a root-finding algorithm which works by repeatedly dividing an interval in half and then selecting the subinterval in which the root exists.
		The bisection algorithm is then applied to the sub-interval where the sign change occurs, meaning that the bisection algorithm is inherently recursive.
		The bisection method is less efficient than Newton's method but it is much less prone to odd behavior.
	en.wikipedia.org /wiki/Bisection_method (337 words)

	The Bisection Method
		The bisection method is one of the bracketing methods for finding roots of equations.
		Investigate the result of applying the bisection method over an interval where there is a discontinuity.
		Apply the bisection method for a function using an interval where there are distinct roots.
	math.fullerton.edu /mathews/n2003/BisectionMod.html (203 words)

	Morphogenesis and Organogenesis in the Regenerating Planktotrophic Larvae of Asteroids and Echinoids -- Vickery et al. ...
		Surgically bisected pluteus larva of the irregular echinoid Dendraster excentricus.
		Seven days after bisection, the newly formed coeloms are clearly separated from the newly formed gut in the anterior portion (D), further extension of the right and left coelomic pouches is evident, and the lost mouth has completely regenerated (G).
		About 7 days after bisection, a lateral view of the anterior larva (D) shows complete regeneration of a secondary juvenile (adult) rudiment, during which the larval arms are absorbed, suggesting a progression of the process of metamorphosis.
	www.biolbull.org /cgi/content/full/203/2/121 (5664 words)

	Bisection -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		For the numerical analysis algorithm, see (Click link for more info and facts about bisection method) bisection method.
		In (The pure mathematics of points and lines and curves and surfaces) geometry, the concept is limited to divisions into two equal parts, usually by a (A spatial location defined by a real or imaginary unidimensional extent) line, which is then called a bisector.
		In classical geometry, the bisection is a simple (Click link for more info and facts about ruler-and-compass construction) ruler-and-compass construction, whose possibility depends on the ability to draw circles of equivalent radius and different centers.
	www.absoluteastronomy.com /encyclopedia/b/bi/bisection.htm (669 words)

	BISECTION, MYOMECTOMY AND CORING IN VAGINAL HYSTERECTOMY OF LARGE UTERUS (Site not responding. Last check: 2007-11-07)
		Bisection was the most frequently used technique in all but one patient.
		Cervix was grasped by volsellum bilaterally and the uterus was bisected in antero-posterior direction with knife with progressive reposition of volsellum till the fundus was reached and pedicles clamped.
		Morecellation of large fibroid was done in one case along with bisection of uterus helping in decreasing the bulk and delivery of the uterus into the vagina.
	www.bhj.org /journal/1999_4104_oct99/original_706.htm (1400 words)

	PRC Bisection Tests
		In the PRC bisection tests, we repeatedly cut in half the circular distribution of the initial phase-states of the oscillator when stimuli are given.
		The null hypothesis of a random distribution of phase responses by initial phase is tested with a Monte Carlo procedure, which bisects random combinations of phase shifts with initial phases, thus determining the probability of the null hypothesis that the observed D score was from a random distribution.
		The bisection procedure can also be used to examine whether stronger phase shifts are produced in one phase response curve than in a contrasting curve.
	repositories.cdlib.org /ucsdpsych/1 (333 words)

	Graph Bisection (Site not responding. Last check: 2007-11-07)
		The decision problem for minimum bisection, which asks for a given graph whether it has a bisection of less than a given width, is obviously in NP since given a bisection we can verify quickly its width and the fact that it is a bisection.
		Given a graph G with n vertices, we claim that the width of the maximum cut for G is equal to that of the maximum bisection of the graph G' given by appending n isolated vertices to G.
		The performance ratio is defined as the ratio of the average bisection found by an algorithm to the average minimal bisection within a class.
	www.cs.berkeley.edu /~szewczyk/cs270 (4719 words)

	Numerical Root Finding
		The idea of the bisection method is based on the fact that a function will change sign when it passes through zero.
		By evaluating the function at the middle of an interval and replacing whichever limit has the same sign, the bisection method can halve the size of the interval in each iteration and eventually find the root.
		To improve the slow convergence of the bisection method, the secant method assumes that the function is approximately linear in the local region of interest and uses the zero-crossing of the line connecting the limits of the interval as the new reference point.
	www.efunda.com /math/num_rootfinding/num_rootfinding.cfm (482 words)

	Bisection Method Tutorial
		The bisection method is discussed in Chapter 9 as a way to solve equations in one unknown that cannot be solved symbolically.
		To solve this equation using the bisection method, we first manipulate it algebraically so that one side is zero.
		The bisection method locates such a root by repeatedly narrowing the distance between the two guesses.
	www.cs.utah.edu /~zachary/isp/applets/Root/Bisection.html (718 words)

	Line versus representational bisections in unilateral spatial neglect -- Ishiai et al. 69 (6): 745 -- Journal of ...
		bisection was compared with that in the line bisection with cueing.
		Table 4 and figure 2 show the results of the bisection tasks for the four patients examined in the right condition.
		The effect of length was similarly found in the line bisection with cueing and the representational bisection (table 4).
	jnnp.bmjjournals.com /cgi/content/full/69/6/745 (3358 words)

	Dissociation of sensory-attentional from motor-intentional neglect -- Na et al. 64 (3): 331 -- Journal of Neurology, ...
		The lines for the bisection task were 230 mm in length and 3 mm thick.
		Ten line bisections and one to three cancellations were obtained in both the direct and indirect conditions.
		In the direct condition, the mean bisection error was rightward for all patients.
	jnnp.bmjjournals.com /cgi/content/full/64/3/331 (4503 words)

	The bisection bandwidth of a network (Site not responding. Last check: 2007-11-07)
		The bisection bandwidth of a network is a measure that is calculated by dividing the network into 2 roughly equal parts, each with half of the nodes.
		One reason that the bisection bandwidth is important is that we can use it to help in quantifying the flexibility in the network.
		In other words, if we have a higher bisection bandwidth, then we have more possible routes that can be used in sending messages between nodes.
	www.cs.utk.edu /~symons/bisection_bandwidth.htm (147 words)

	The Bisection Method (Site not responding. Last check: 2007-11-07)
		The bisection method is developed with the support of the Intermediate-Value Theorem, 1.3.
		At each step the interval in which there is guaranteed to be a root of the equation is halved (bisected), and the method terminates as soon as the width of the interval containing the root is less than some error tolerance
		Since the bisection method keeps a bounded interval where there is at least one root at each step, it falls in the category of bracketing methods.
	www.mathcs.emory.edu /ccs/ccs315/ccs315/node14.html (248 words)

	Bisection Of Eccentricity
		In this case, by “bisection of eccentricity”, it refers to the situation where Ptolemy places the equant point on the mirror image of E along the line of apsides such that
		The former is half the value of the latter because of the difference in the way Kepler and Ptolemy had measured the separation between Sun and Earth on their respective solar models.
		In summary, we see that “bisection of eccentricity” either refers to Ptolemy splitting the total eccentricity exactly into two on his planetary theory, or refers to Kepler dividing the solar eccentricity as defined in Ptolemy’s (or Hipparchus’) solar theory.
	www.math.nus.edu.sg /aslaksen/projects/heilbron/Bisection_Of_Eccentricity.htm (420 words)

	Heterostaura allopola
		We start with a bisection of a straight rectangular four-sided pyramid (the base of which is a rectangle, and having its tip right above the center of that rectangle, causing the main axis to be a 2-fold rotation axis).
		Indication of an i d e a l bisection of the polygon of Figure 25 representing the basic form of the Octophragma (Autopola oxystaura with eight antimers).
		Indication of an i d e a l bisection of the polygon of Figure 38 representing the basic form of the Tetrakaidecaphragma (Autopola oxystaura with fourteen antimers).
	home.hetnet.nl /~turing/allopola.html (5466 words)

	First Steps in Numerical Analysis (Site not responding. Last check: 2007-11-07)
		In either Case 2 or Case 3, the process of bisection of the interval containing the root can be repeated until the root is obtained to the desired accuracy.
		The bisection method is almost certain to give a root.
		One drawback of the bisection method is that it applies only to roots of f about which f (x) changes sign.
	kr.cs.ait.ac.th /~radok/math/mat7/step7.htm (603 words)

	Bisection Method (Site not responding. Last check: 2007-11-07)
		The Bisection method is a bracketing method that is used for finding a zero on a continous function.
		The Bisection Method is a slow but reliable method of finding a zero of a function.
		The bisection method systematically moves the endpoints closer and closer until the an interval of arbtarily small width is obtained such that f(a) or f(b) approximately zero.
	jewel.morgan.edu /~sbutler/bisect.html (453 words)

	Bisection Methods:
		Hence we choose the subinterval [1/3,2/3] and bisect it further.
		We approximate the root at this stage as the arithmetic average of the end-point coordinates of this interval, this gives for the root
		Thus the choice of starting interval is important to the success of the bisection method.
	web.mit.edu /10.001/Web/Course_Notes/NLAE/node2.html (362 words)

	LAB #4: Fast & Dangerous Root Finding
		For the bisection method, the most natural test is on the size of the change-of-sign interval.
		Regula Falsi is very similar to the bisection method: it assumes that we start with a change of sign interval, and each step of the method tries to make this interval smaller.
		Richard Brent devised a routine that combines the reliability of bisection with the speed of the secant method, and added another method that can be faster yet.
	www.csit.fsu.edu /~burkardt/math2070/lab_04.html (1903 words)

	Bisection Method E-book Nonlinear Equations (Site not responding. Last check: 2007-11-07)
		Bisection Method, Numerical Solution of Nonlinear Equations, Mathcad, Maple, Mathematica, Matlab, Simulations.
		Table 1: Root of f(x)=0 as function of number of iterations for bisection method.
		classroom presentation video of the background and algorithm of the bisection method.
	numericalmethods.eng.usf.edu /mcd/gen/03nle/mcd_gen_nle_lea_bisection.htm (847 words)

	Bounds on the Bisection Width for Random (ResearchIndex) (Site not responding. Last check: 2007-11-07)
		The upper bounds are obtained from the analysis of the performance of a randomized greedy algorithm to nd bisections of d-regular graphs.
		We also give empirical values of the size of the bisection found by the algorithm for some small values of d and compare it with numerical approximations of our...
		2 Bounds on the max and min bisection of random cubic and rand..
	citeseer.ist.psu.edu /702984.html (540 words)

	The Method of Bisection
		In the method of bisection, we approximate a solution of the equation f(x) = 0, where f(x) is a continuous function, by means of a successive reduction of intervals that contain the solution.
		The method of bisection will always produce an approximation of a root of a continuous function f(x) provided one can find values a and b, in the domain of f(x), such that f(a) < 0 and f(b) > 0.
		Because of this, the method of bisection is commonly utilized for the purpose of reducing the size of the interval on which a root of a given function is known to exist, and then an alternative method of root approximation is utilized to bring the approximation to within the desired amount of accuracy.
	www.mathcs.emory.edu /ccs/ccs215/roots/node2.html (875 words)

	Data Mining Graph Clustering: Hierarchical Clustering
		After that the bisection heuristics is run on the contracted graph to obtain the bisection.
		After such bisection (A',B') is obtained, the edges are uncompacted from the original graph and an initial bisection (A,B) is created for the original graph.
		Finally this original bisection is used as a starting configuration for the bisection procedure on the original graph.
	www-users.cs.umn.edu /~sushrut/research/pub/cover/node24.html (1730 words)

	Abstract: A Local Graph Partitioning Heuristic Meeting Bisection Bounds (Site not responding. Last check: 2007-11-07)
		The partitioning of a graph into several clusters is often done by recursive bisection.
		Bisection heuristics are usually divided into global and local methods.
		In this paper, we will present the HS-idea, the bisection heuristic, ideas of the proofs of upper bounds, and, finally, discuss the performance of the method compared to other heuristics.
	www.uni-paderborn.de /fachbereich/AG/monien/PUBLICATIONS/ABSTRACTS/MD_HeurBisBounds_PP97.html (184 words)

	[No title] (Site not responding. Last check: 2007-11-07)
		This procedure will recursively # bisect a function, added particular plots to the final plot to be # displayed.
		bisection := proc(func,bottom_point,top_point,level) # local variables local middle_point, interval_plot: # calculates the middle point middle_point := (bottom_point + top_point) / 2: # If the point which is above the x-axis is before the jpoint that is # below, create the plots appropritately.
		RETURN(plots[display](set_of_plots union {plot(func(t),t=left_range..right_range,axes = NORMAL)})): end: # Create the bisection example with the function x->sin(x), # Starting points of the Bisection as 1, 4 and left and right parts # of the graph being 0 and 2 Pi.
	www.cecm.sfu.ca /~kghare/numeric/maple/bisection (364 words)

	Perceptual Learning of Spatial Localization: Specificity for Orientation, Position, and Context -- Crist et al. 78 (6): ...
		To determine whether learning of the bisection discrimination task is specific for the orientation of the stimulus used during
		bisection task is specific for the trained orientation.
		We have shown that improvement on the bisection task is specific for the attribute of the stimulus analyzed during training
	jn.physiology.org /cgi/content/full/78/6/2889 (3963 words)

	LAB #3: Roots of Equations
		Inside of the bisection code, we should probably evaluate the function at both points, and save these values in FA and FB.
		The bisect routine treats the endpoints of the interval as variables, and gives them "dummy names" that we fill in when we use the routine.
		When you are done, prepare a short table with the function number, the computed root, and the number of steps, and mail it to me. You should finish this assignment, and mail me the results, before our next class on 22 September.
	www.csit.fsu.edu /~burkardt/math2070/lab_03.html (1254 words)

	Journal of Vision - The consistency of bisection judgments in visual grasp space, by Trommershäuser, Maloney, & ...
		We study whether bisection in visual grasp space (the region over which eye and hand can work together to grasp or touch objects) depends on fixation or on the method of judgment employed (the task).
		When observers maintained fixation (on an endpoint or in the neighborhood of the bisection point), fixation location had a small but significant effect on bias, although those effects were small compared with bisection uncertainty.
		We conclude that bisection judgments differ significantly between fixations, but that the effect of fixation location on bisection is not large enough to be detected reliably by the observer moving his or her eyes during a judgment.
	www.journalofvision.org /3/11/13 (267 words)

	bisection search
		A bisection search is a simple search algorithm which may be used to solve an equation
		To see how a bisection search works, suppose the first derivative is positive.
		Provided f(x) is monotonic in x, this solution algorithm will usually require fewer trials than the "shotgun approach".
	www.in-the-money.com /glossarynet/bisectio.htm (228 words)

Try your search on: Qwika (all wikis)