Questions tagged [bisection]

Use this tag for questions related to the bisection method, which is a root-finding method that repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing.

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The function defined by $f(x)=\sin (\pi x)$ has zeroes at every integer.

The function defined by $f(x)=\sin (\pi x)$ has zeroes at every integer. Show that when $-1<a<0$ and $2<b<3$, the bisection method converges to $0$, if $a+b<2$. How to approach this? ...
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2answers
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How do I solve $y=x+B\sin(x+A)$ for $x$

I have a code that converts x into y using the formula: $y=x+B\sin(x+A)$ with $x, A$ and $B$ known values. $B$ is also very small so that $B\sin(x+A) < 0.035$. The problem is that in another ...
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63 views

Why does the “shooting” or “wag the dog” method give a bound state?

I am using numerical methods to solve Schrodingers equation. I have identified an interval for E (energy) in which one solution tends to infinity, but on the other side the other solution tends to ...
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1answer
45 views

Which zero bisection method locates?

This regarding an exercise from the Numerical Analysis book by Conte and de Boor. The question is the following. If $a$ and $b$ are such that $f(a)f(b)<0$ and if $f$ has more than one zero in $(a,...
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1answer
77 views

Obtain an aproximation to $\sqrt{5}$ using other numeric methods

From the original problem: Find an approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ using the bisection algorithm. In which I have a function in Mathematica to do the ...
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1answer
71 views

Approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ [duplicate]

I am attempting to resolve the following problem: Find an approximation to $\sqrt{5}$ correct to an exactitude of $10^{-10}$ using the bisection algorithm. From what I understand, $\sqrt{5}$ has ...
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38 views

Root finding algorithms for complex functions

Is there an analogue for bisection (or the golden section method), i.e., solving $f(x) = 0$ when $f:\mathbb{R} \rightarrow \mathbb{C}$. When $f$ is real-valued, we know (at least one) root exists ...
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1answer
36 views

Bisection Newton - Quadratures

The problem states the following: Find with at least 10 digitis of precisión the roots of the following equation: $\int_x^{x^2} \!e^{-t^2}\,\mathrm{d}t = x^5 -3x^2 + 1 $ in the closed Interval [-1,1]. ...
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Bisection Method vs Newton's [duplicate]

Why is Newton's root finding method faster than the bisection method? I cant seem to find a good explanation besides calculations of the error through each iteration of each algorithm and comparing ...
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1answer
228 views

How to calculate order and error of the bisection method?

I have a problem understanding 3 (related) things here. First attachment: 1) Let's say (a) would be the line in the screenshot "error = current root - actual", and (b) the next line with en+1= M*...
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4answers
161 views

Using Euclid Elements, is it possible to bisect a line at an angle other than 90 degrees?

From Euclid's Elements, Book 1, Proposition 10 shows that, the line is bisected at right angles. Is it possible to bisect a line at any angle other than 90 degree?
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110 views

Incenter of a Triangle.

In triangle ABC, bisectors $AA_1$, $BB_1$ and $CC_1$ of the interior angles are drawn. If $\angle ABC=120^ \circ$, what is the measure of $\angle A_1B_1C_1$ ? I solved this problem as : Mark D, as ...
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1answer
142 views

Bisection method nth root

Given three roots $$ \text{Single }\alpha_1 = -1,\quad \text{Double }\alpha_2 = 0,\quad \text{Triple }\alpha_3=1 $$ A root α of a continuous function f can be approximated using the bisection ...
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1answer
175 views

Euler method and bisection method

I'd like to solve the equation $$ \phi''(x) = \lambda \sin (\phi(x)) $$ where $x \in (0,L)$, $\phi'(0) = 0$, $\phi'(L) = 0$. Let $ \psi = \phi'$ and $$ \phi'(x) - \psi(x) = 0$$ $$ \psi'(x) - \lambda ...
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141 views

Can I use Bisection search method to find the maximum of following kind of function?

I have a function $f(x)$ defined over $0<x<\bar{x}$. The function is negative for $0\leq x<x_L$ and then it becomes positive for certain range of $x$ $x_L\leq x<x_U$. Further, I know that ...
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0answers
698 views

Use the bisection method to find the minimum of the function

Use the bisection method to find the minimum of the function is $f(x)= 3x^2–4x+1$ over the interval $[0,2]$ . Determine the optimal value of $x$ within $5\%$ of the initial interval and How many ...
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3answers
509 views

How can I calculate the perpendicular bisector of a vector?

I have seen questions and examples on how to calculate this which returns an equation, but how would I then apply this equation to calculate the actual vector of the perpendicular bisector? In my ...
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1answer
49 views

Bisecting geo problem - from Art of Problem Solving

$I$ is the incenter of $\triangle ABC$. Lines $BI, CI$ meet the line parallel to $BC$ through $A$ at points $D, E$. The perpendicular bisectors of segments $BD, CE$ meet $BC$ at points $X, Y$. a) ...
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1answer
72 views

In the quadrilateral abcd, bd is the bisector of angle d. If c = 30, ad = 2, bc = 4 and cd = 6, then what is the area of ​the quadrilateral abcd?

In the quadrilateral abcd, bd is the bisector of angle d. If c = 30, ad = 2, bc = 4 and cd = 6, then what is the area of ​​the quadrilateral abcd?
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1answer
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Stopping criteria when using the bisection method

I'm working on old exams in basic numerical modeling. The problem is: $2x \ - e^{-x}=0 $ has a root in the interval $(0, 1.6)$. Find it with an error less than $0.02$ using the Bisection method. ...
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1answer
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Proof of bisection Fibonacci formula [closed]

This is the formula of a bisection sequence of Fibonacci: $$F(n) = 3 \cdot F(n-1) - F(n-2); \quad F(0) = F(1) = 1$$ https://oeis.org/A001519 How can i prove that this formula works for each $n>1$...
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Proof that length of opposite side to angle bisector is $p=bc/(a+b)$

Given triangle $ABC$ with angle $C$ bisected to meet side $c$, we have the following sides of the triangle: $a$, $b$, $c$, $x$, $p$, and $q$ where $x$ is the angle bisector, $p+q=c$ (the two divisions ...
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2answers
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Quickest way to find a point at a certain distance on the angle bisector

Here's the for reference. The objective is to find the point (xc,yc) when (x1,y1), (x2,y2), (x3,y3) and 'd' are known. My present approach is as follows. Find the dot product of the lines described ...
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2answers
87 views

How does my prof's logic work? Find four roots of $p(x)$.

Below is the solution to a problem where you have to find four intervals of length $1/16$ that contain roots of $p(x)$. Apparently, Since the cubic and quadratic terms have large negative ...
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2answers
427 views

Angle Bisectors in a Triangle

My son got this problem in geometry and was stumped. He asked me and I am stumped too. Here is the problem: In triangle ABC, m∠ACB = 42°. The angle bisectors AD and BE intersect at point O so that AE ...
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1answer
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bisection method's values

I've implemented bisection method. When I run the function, the values keep increasing, and there's never a negative value. also, if condition is altered either value of a or b won't change. ...
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0answers
127 views

MatLab Bisection method - updating the limit for each iteration[help]

So below I have a written function emplyoing a bisection algroithm for finding roots. One issue I have(if you can't find more that will say) is that I don't know how to incorporate a new limit for ...
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2answers
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quadrilaterals, bisectors are parallel [closed]

prove that in a quadrilateral ABCD with angle B=90 and D=90 the bisectors of A and C are parallel. ABCD is not a rectangle
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1answer
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Find bisector equation using a point the bisector goes through and an angle

I am given a triangle with vertices $A=(0,0)$, $B=(-7,0)$ and $C=(0,4)$. This is a right triangle. One might think from graphing that the angle bisector cuts from point B and point $(0,2)$ but this is ...
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1answer
205 views

Bisection Method - Some Cases

Now I have a working code for Bisection Method but there are some cases I want to handle 1- The boundaries of trial: Can we put a negative interval? ex. start with f(-5) and end with f(5) ? 2- If we ...
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1answer
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What can be said about the convergence rate of the bisection method?

Bisection method is commonly said to be linearly convergent, but as far as I can tell, it does not neatly fit into the definition. e.g. a method is convergent with order $\alpha$ if $|x_{n+1}-x^*|\le\...
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2answers
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Bisection Method for functions just touching $x$-axis

For functions just above or below x-axis like $f(x)=x^2$ or $f(x)=|x|$, is there any way to use bisection methods? Is using something like $x=y+2$ and $f(y+2)=(y+2)^2$ and then solving for $y$ to ...
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2answers
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bisectors in a right triangle

Given right triangle $ABC$, $AC=8$, $BC=6$ and $\angle C = \frac{\pi}{2}$. $BP$ and $CR$ – bisectors of triangle $ABC$, intersecting at the point $L$. Need to find: 1) periods in which these ...
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1answer
150 views

Optimal step size update in generalized bisection method

Let $[a,b]$ be some interval, and let $X \in [a,b] $ be some unknown number one would like to find (approximately). An example of this problem is finding the root of a real function which changes its ...
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3answers
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Asymmetric bisection

I have this problem which I believe is pretty simple, however I'm not finding anything online. I need to find a zero of a function numerically. I know that $f(0)<0$ and $f(1)>0$ and that $f(x)$ ...
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2answers
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Find bisection iterations based on number of decimal places

Given the equation: f(x) = x3 - x - 2 and the interval (1,2) I was asked to calculate the iterations that are going to be needed in order to get the root at 4 decimal places I know how to apply the ...
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1answer
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subgradient of one-dimensional least absolute difference

I am trying to solve the following one-dimensional least absolute difference (LAD) optimization problem and I am using bisection method to find the best beta (a scalar). I have the following code: <...
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Bisection-Regula falsi-Bolzano

I want to ask about these theorems in Matlab, to confirm the requirement that x1, x2 where f(x1) * f(x2) < 0 is there any way to find x1, x2 if i have the function eg. $$f(x) = \tan(x)\frac{(e^{2x} ...
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Intervals for bisection method

I have this function below: $$f(x) = \tan(x)\frac{(e^{2x} - 1)}{(e^{2x} + 1)} + 1$$ and I want to find the intervals to use the bisection method. The first interval I think is $f(0) = 1 >0$ but i ...
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Bisection method to $f(x) = \cos(x) - xe^{x}= 0$ .

I was doing an example of Bisection method applied to $f(x) = \cos(x) - xe^{x}= 0$, I did all correctly upto 4th step , but after that i don't understand how it is considering the interval of $(0.5,...
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2answers
934 views

What is "find a solution accurate to within 10^-4 mean in Bisection method?

If I for example after "9" iterations get the following : p_9 = 1.365234375 and the actual p is given as: p = 1.365230013 Is it simply saying that p_9 is within 10^-4 because the first 4 numbers 1....
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1answer
82 views

Calculation error the length of an angle bisector

How to find the length of an angle bisector ($BK$) in a triangle $A(1;4),~B(7;8),~C(9;2)$. I use this formula: $\frac{A_{1} \cdot x+B_{1} \cdot y+C_{1}}{\sqrt{A_{1}^{2}+ B_{1}^{2}}}=\frac{A_{2} \...
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2answers
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What is the formula for bisector of triangle? [closed]

Triangle $ABC$: $A(1;4), B(7;8), C(9;2)$. $BK is$ bisector of triangle. What is the formula?
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0answers
331 views

Solving an optimization with Bisection algorithm

Basically, I have an S-shape quasiconvex function which becomes a straight line at its end points. Can bisection algorithm handle these points to find an optimum? $f(t)=a e^{-b e^{-c (t-d)}}$ If yes ...
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1answer
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Formula for bisector segment of a given lenght between two segments

I've got the (x,y) coords of three points defining two connected segments; I need to find the coordinates of the two bisectors, of a chosen lenght, at the angle between the two segments. I have ...
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1answer
2k views

What is a proof that a diameter bisects a circle?

One of the major contributions Thales is said to have given is the proof that a diameter of a circle bisects the circle, yet Euclid doesn't even bat an eye. Then again, Euclid skipped over other ...
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1answer
52 views

Find the value of $MF^2$ with the given information

Acute triangle $ABC$ has orthocenter H. The foot of the altitude from $C$ to $AB$ is point $F$ and the foot of the altitude from $A$ to $BC$ is $D$. Let $M$ be the midpoint of $AC$ and let $N$ be that ...
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1answer
434 views

Two chords in a circle cut each other up into equal line segments. What's the radius of the circle?

I may be remembering the question wrong. It went something like Two chords in a circle split each other up into equal line segments of 1 and 3, respectively. Find the radius of the circle. which I ...
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1answer
108 views

How can i run my bisection code in matlab what are error in my code?

Your code bisection.m ...
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2answers
99 views

What does the length of BP approach?

Given isosceles triangle $ABC$ below with $\angle{B}=\angle{C}$ and $BC=1$. Let point $P$ be the intersection of the line bisecting $\angle{B}$ and $AC$. Determine the length of $BP$ as the length of $...