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Results tagged with Search options answers only user 2150
14 results
MATLAB has a built-in function lsqnonneg() which is an implementation of the active set method described in the book "Solving Least Squares Problems" by Lawson and Hanson (1974) The \ solution of l …
answered Nov 11 '13 by Brian Borchers
If $A$ is of full column rank and $A^{T}A$ is non-singular and well-conditioned, then you can compute the pseudoinverse as: $A^{\dagger}=(A^{T}A)^{-1}A^{T}$. This will be faster than computing a …
answered Sep 5 by Brian Borchers
If you have access to the MATLAB optimization toolbox then this can easily be done using the quadprog() function. You'd start by writing the objective in quadratic form as $\| Ax - b \|_{2}^{2} = … answered May 9 '14 by Brian Borchers Others have already supplied the two most likely answers to this question, but I'll add a bit of comparison and a way to help decide between the two approaches. I'd suggest either A primal-dual in … answered Jul 23 '14 by Brian Borchers Neither of these approaches is recommended. Although pivoted Cholesky factorization can help with badly conditioned matrices, it ultimately won't help with a singular matrix. The modified Cholesky f … answered May 29 by Brian Borchers Minimizing the 2-norm of$x$among all least squares solutions is relatively easy to do- this is the pseudoinverse solution. It can be computed using either a rank revealing version of the QR factori … answered Apr 2 '14 by Brian Borchers The notation here is very confusing, and that's probably the main cause of your difficulty in formulating this as a linear least squares problem. Introduce the notation$\mbox{vec}(x)$for the$mp$… answered Apr 22 '14 by Brian Borchers In general, you can formulate this as a nonlinear least squares problem. If your values are known at points$(x_{i},y_{i})$, and the known values are$f_{i}$, then you can minimize$\min_{a,b,c,d,e} …
answered Dec 6 '17 by Brian Borchers
This isn't a linear least squares problem as it is written. However, the problem does simplify down to a quadratic optimization problem with nonnegativity constraints and you can even write it as a l …
answered Feb 14 '14 by Brian Borchers
If we let $\phi(x)=\sum_{i=1}^{m} F_{i}(x)^{2}$, we could compute $\nabla \phi(x)$ by finite difference approximation. However, it is generally smart to make use of the special structure of $\phi … answered Mar 29 '18 by Brian Borchers If$N$is on the order of 100,000 and$m$is on the order of$100$, Then$J$requires about 80 gigabytes to store in double precision and$V$requires a trivial amount of storage. The product$M=JV$… answered Jun 30 '18 by Brian Borchers Your problem is still a linear least squares problem. You can write$\Psi(x)$as$\Psi(x)=\| Hx - g \|_{2}^{2}$where$H=\left[ \begin{array}{c} I \\ M \end{array} \right] $and$g=\left[ \be …
answered Feb 24 by Brian Borchers
How would you solve the problem if you didn't need to do the centering? Since $A$ is large and sparse, you'd probably pick an iterative method such as CGNE which depends on being able to perform ma …
answered Aug 25 '18 by Brian Borchers
You can reformulate this problem as a conventional linear least squares problem as follows: First, write $YCZ$ as $YCZ=\sum_{i=1}^{p} \sum_{j=1}^{m} C_{i,j} (Y_{:,i}Z_{j,:})$ Next, define the \$\mb …
answered Nov 26 '17 by Brian Borchers