equation-solving

In a C++ application I'm coding, I need to solve a system of non -linear equations (N equations, N unknowns). The systems I'm solving will be rather small (up to 10 equations/unknowns), so performance is not going to be a real issue. I've searched the web a bit for a non-linear solver library, and I couldn't get to something which looks easy to use (got to NOX and C/C++ Minpack , but both seem to be an overkill for my need). Any thoughts and ideas of easy-to-use libraries for this purpose? There are two options for you, you can use the sundials packages which includes a nonlinear solver,

I am trying to find intersection points of two curves syms x y g(x) = 20*(exp(-(x+30)/3.5)-1); [sol_x, sol_y] = solve((x+22.3097)^2+(y+16.2497)^2 == 25, y == g(x),x,y,'Real',true) ; It is giving only one solution. But according to the plot of the two equations, there should be two intersection points. How can I rectify this problem? The solver can not find a analytic solution, thus a numeric solver is used. There is no reliable way in finding all solutions with a numeric method, but if you have a good guess (e.g. from a plot) try vpasolve with a reasonable set initial value. In this case, with

I have a system of under-determined linear equations Ax = b (i.e. more unknowns than equations) that I would like so solve in matlab. I know that this would usually mean an infinite number of solutions, but I also know the solutions should be positive integers and less than a certain number. Can I find all the solutions that meet those additional requirements? This problem come from having an unknown matrix where I know the sum of each row and column. e.g. unknown matrix to find 0 3 2 0 0 2 4 1 2 1 0 0 Row sums known 5 7 3 Column Sums know 2 6 6 1 I've tried the lsqnonneg(A,b) function which

Which algorithm you would recommend for fast solution of dense linear system of fixed dimension (N=9) (matrix is symmetric, positive-semidefinite)? Gaussian elimination LU decomposition Cholesky decomposition etc? Types are 32 and 64 bits floating points. Such systems will be solved millions of times, so algorithm should be rather fast with respect to dimension (n=9). P.S. examples of robust C++ implementations for proposed algorithm are appreciated. 1) What do you mean by "solved million of times"? Same coefficient matrix with a million of different right hand terms, or a million of distinct

I am coding a function that solves an arbitrary number of simultaneous equations. The number of equations is set by one of the parameters of the function and each equation is built from a number of symbols - as many symbols as there are equations. This means that I can't simply hardcode the equations, or even the symbols needed to put together the equations; the function needs to be able to handle any number of equations. So, my question is, how do I produce a list of symbols? I have one possible solution, but my gut tells me that it's not going to be very efficient. Please let me know if

Suppose I have the following equations: x + 2y + 3z = 20 2x + 5y + 9z = 100 5x + 7y + 8z = 200 How do I solve these equations for x , y and z ? I would like to solve these equations, if possible, using R or any other computer tools. This should work A <- matrix(data=c(1, 2, 3, 2, 5, 9, 5, 7, 8), nrow=3, ncol=3, byrow=TRUE) b <- matrix(data=c(20, 100, 200), nrow=3, ncol=1, byrow=FALSE) round(solve(A, b), 3) [,1] [1,] 320 [2,] -360 [3,] 140 For clarity, I modified the way the matrices were constructed in the previous answer. a <- rbind(c(1, 2, 3), c(2, 5, 9), c(5, 7, 8)) b <- c(20, 100, 200)