# Tagged Questions

52 views

### Best approximating linear polynomial for $|x|$ on $[-1,5]$ [on hold]

How to find the best approximation polynomial $p_1(x)\in P_1$ for $|x|$ on $[-1,5]$ w.r.t. $\|\cdot\|_{\infty}$? I want to use the Equioscillation theorem but have no clue.
39 views

### How do you derive the secant method formula from the equation below?

The Secant Method forumula is; $$x_{i+1}=x_i - \frac{f(x_i)(x_i-x_{i-1})}{f(x_i)-f(x_{i-1})}.$$ Derive the formula from the equation below; ...
33 views

### I am not sure how to use the secant method formula without a function being given?

Calculate an approximation value for $4^{\frac34}$ using four steps of the secant method with the starting values of $x_0=3$ and $x_1=2$.
40 views

### Can someone explain in general what a central difference formula is and what it is used for?

Topic- Numerical Approximations
44 views

### Firstly what is an $O(h^3)$ formula? Also I am not quite sure how to answer the question?

The forward-difference formula can be expressed as $$f'(x_0)=\frac{1}{h}(f(x_0 +h)- f(x_0))-\frac{h}{2}f''(x_0) - \frac{h^2}{6}f'''(x_0) + O(h^3).$$ Use Richardson's extrapolation to derive an ...
43 views

### Which (approximative) methods are there to compute the inverse of a complicated function?

I have a complicated function $f(x)$ for which I want to compute the inverse $f^{-1}$ over a certain range $R(f): a \leq f(x) \leq b$. The only way to find the inverse I can think of is power series ...
115 views

### How could I improve this approximation?

In a computer application, I need to solve trillions of times an equation which can be reduced to $$f(x)=\sin(x)-a x=0$$ Newton methods (quadratic and higher orders) are used for the solution. ...
31 views

### Newton-Cotes Quadrature formula

Im trying to find more information about numerical integration methods. When is a Newton-Cotes Quadrature formula on n nodes exact?
23 views

### Looking for a approximation/solution to my mortgage calculator function

I'm working on a little function, $t(A,y,r)$ that calculates the monthly payment of a fixed-rate mortgage, where $A$ is the amount borrowed, $y$ is the number of years over which the loan will be ...
49 views

### How obtain a (accurate) function from this graph with these points?

I need obtain the function from 0 to 20 from this graph: I have the even numbers in the {x, f(x)} format: {0, 0}, {2, 1.8}, {4, 2}, {6, 4}, {8,4}, {10,6}, {12,4}, {14,3.6},{16,3.4}, {18,2.8}, ...
30 views

### Estimating the absolute error of the function $f(x)=4x^2$

I have to estimate the value of $f(x)=4x^2$ for $x\in [1,2]$, and $x$ is unknown. the approximated value for $x$ is $\tilde x$, which is also in $[1,2]$. What is the maximum absolute error of $x$, ...
64 views

31 views

### Is the following statement on the stability of the forward Euler method true or false?

My text asks whether the following statement is true or false: The forward Euler method for approximating the solution of $x'=\lambda x$ is stable for all $\lambda \in \mathbb R$ and all step ...
52 views

### Simplify function with polynomial via least-squares

I want to "adjust" (simplify) $f(x)$, a function, by $g(x)$, a polynomial, via least-squares. I want to write code for that. Apperently my code is issuing wrong results, so I was wondering if my ...
102 views

### Solve non-linear equations of 3 variables using Newton-Raphson Method iterms of c,s and q.

The three non-linear equations are given by $$c[(6.7 * 10^8) + (1.2 * 10^8)s+(1-q)(2.6*10^8)]-0.00114532=0$$ s[2.001 *c + 835(1-q)]-2.001*c =0 ...
59 views

### Change of variable

I have to approximate the following integral, using Simpson's Composite $1/3$ Rule: $\displaystyle \int\limits_{0}^1 \mathrm{\frac{e^{2x}}{\sqrt[5]{x^2}}}\,\mathrm{d}x$. The only problem is that ...
37 views

### Comparison of trapezoidal , Simpson's 1/3 ,Simpson's 3/8 and Boole's rules.

These rules are often used in numerical integration. How do we analyze the given support points or function and select the most suitable one for best approximation?
54 views

### Numerical solution of non-linear differential equation with MATLAB

I need some information to know if I can solve a nonlinear integral equation with terms $u_{x}$ , $u_{x}.u_{y}$ , $u_{xx}$ , $u_{xy}$ $u_{yy}$ $u_{x}^{2}$ $u_{y} ^{2}$ By numerical ...
56 views

### Is it possible to calculate $e^x$ given $2^x$?

Given a value $x$, if I have a microprocessor instruction that will give me the value of $2^x$, is it possible to calculate (or approximate) the value of $e^x$ ?
30 views

### Initial approximation to inverse of beta distribution function / quantile of beta distribution

I'm interested in implementing an algorithm to find the quantile of the beta distribution, and I'm looking at this paper: Journal of the Royal Statistical Society Series C (Applied Statistics). 1973, ...
79 views

### Approximating $\sqrt{101}$ using Taylor series methods

I'm trying to approximate $\sqrt{101}$ using the Taylor series for the function $f(x)=\sqrt{x}$ centered at the point $x=100$. I need to obtain an approximation that is within $0.01$ of the correct ...
36 views

### division by sum of exponentials of large negative numbers

I need to evaluate the following numerically: $$f = \frac{\exp(a)}{\exp(a)+\exp(b)+\exp(c) + \exp(d)}$$ $a,b,c$ and $d$ are large negative numbers, they are smaller than -1000. Numerically ...
24 views

59 views