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Questions tagged [nonlinear-algebra]

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0answers
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Speeding up the solution of a large set of nonlinear algebraic equations in `sympy`

I have a quite large algebraic equation system to solve, the system is so large, I can't post the example here, so I am posting it to pastebin. The sympy.solve is ...
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1answer
82 views

ill-conditioning

I am struggling with following exercise from book of Nocedal, Numerical optimization, chapter 2, excercise 2.12: Suppose that a function $f$ of two variables is poorly scaled at the solution $x^*$. ...
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0answers
47 views

Nonlinear Sylvester-Like Equation

Maybe you can point me to some results already developed for this. I have to solve for $X$ the following "Sylvester-like" equation: $$ AX - XB = F(X)$$ where $A\in\mathbb{R}^{a\times n}$, $B\in\...
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2answers
235 views

C++ template design pattern for groups (algebra)

Having both programmed my share of c++ and studied some beginners group theory some year ago, I got curious about this... Is there any particularly popular template based (object oriented) design ...
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1answer
710 views

Solving system of 7 nonlinear algebraic equations symbolically

I have a system of seven nonlinear equations that I want to find their symbolic solutions. The solution will depend on the parameter K, and I should have different solutions by varying the parameter. ...
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1answer
155 views

How can i define algebraic equation in differential function in MATLAB?

I want to solve 7 pde's that are functions of time, radius(j) and length(i). I used the method of lines and converted them to a system of odes in time and it becomes something like this: $$dy/dt=((y(i,...
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1answer
153 views

Solving this nonlinear system of equations

Suppose I have this set of equations: $$a = x + z\qquad (1)$$ $$b = y + \frac{z}{2}\qquad (2)$$ $$ z = k_0x\sqrt{y}\qquad (3)$$ Where $a$, $b$ $\in \mathbb{R}$ and $k_0 > 0$. The values of $a$ ...
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1answer
78 views

Solving a pair of high-degree polynomials in two variables with Maple

I have two algebraic equations I am trying to solve in Maple. They are: $14\,{a}^{26}{b}^{2}-91\,{a}^{24}{b}^{4}-364\,{a}^{22}{b}^{6}-1001\,{a} ^{20}{b}^{8}-2002\,{a}^{18}{b}^{10}-3003\,{a}^{16}{b}^{...
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2answers
131 views

Solving a system of polynomial equations with multiple variables

I have a system of equations of the form: $$ l_i^T l_j \cdot m_i^T m_j - m_i^T R l_j \cdot l_i R^T m_j = 0$$ where $R \in \mathbb{R}^{3\times3}$ is an unknown rotation matrix. $l_i, l_j, m_i, m_j \in ...
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1answer
1k views

System of nonlinear equations in MATLAB

I've got some problems solving (numerically) this system of equations. \begin{array}{l} 40 \cdot \cos (2t) + 105 \cdot \cos ({\theta _3}) - 75 \cdot \cos ({\theta _4}) - 91.924 \cdot \cos ({337.62}) =...
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0answers
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Estimating eigenvalues from time-dependent non-linear operator

I have a very sparse non-linear system $N(u) = 0$ that can be solved as a time-dependent ODE, $\frac{du}{dt} = N(u)$, and explicitly integrated until $\frac{du}{dt} = N(u) = 0$, e.g. by forward euler, ...
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1answer
8k views

How do I extrapolate data from a NON-LINEAR (logarithmic) standard curve in Excel?

I have made a standard curve. The X-axis is logarithmic. The y-axis is linear. I have added a logarithmic trendline (y = -1.546ln(x) + 39.254; R² = 0.9906). How can I re-arrange the equation to ...
3
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1answer
86 views

How to pick a basis for the result of a non-linear function given a basis for its argument

I am trying to represent the result of a non-linear function in a small basis, given another small basis that does a good job a representing the argument of the function. More specifically, there ...
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3answers
1k views

Convergence of fixed point iterations of a non-linear matrix system

I'm working on modeling two phase immiscible flow in a porous medium. When I setup the system of equations, I obtain a non-linear system of equations that can be expressed in the form: $A(x)x=b$ ...
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3answers
3k views

Solution of quartic equation

Is there a open C-implementation for the solution of quartic equations: $$ax⁴+bx³+cx²+dx+e=0$$ I am thinking of an implementation of Ferrari's solution. On Wikipedia I read that the solution is ...
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5answers
356 views

Iterative solution to a nonlinear equation

I appologize in advance if this question is silly. I need to compute the root of \begin{equation} u -f(u) =0 \end{equation} Where $u$ is a real vector and $f(u)$ is a real-vector valued function. ...
9
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3answers
993 views

Basin of attraction for Newton's method

Newton's method for solving nonlinear equations is known to converge quadratically when the starting guess is "sufficiently close" to the solution. What is "sufficiently close"? Is there literature ...