When the regression is expressed as a matrix equation, the matrix of regressors then consists of a column of ones ( the constant term ), vectors of zeros and ones ( the dummies ), and possibly other regressors.
42.
In linear-quadratic-Gaussian control, there arises a nonlinear matrix equation for the reverse evolution of a current-and-future-cost " matrix ", denoted below as " H ".
43.
More generally, the term "'Riccati equation "'is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control.
44.
This research accomplishment was awarded the first Cray GigaFLOP Performance Award at Supercomputing'89 . This code evolved into NASA's General-Purpose Solver ( GPS ) for Matrix Equations used in numerous finite element codes to speed solution time.
45.
Then if and only if the rank of the augmented matrix [ " A " | " b " ] is also 2, there exists a solution of the matrix equation and thus an intersection point of the " n " lines.
46.
:Alright, I decided to drastically simplify the problem and made a whole bunch of assumptions . . . I end up with a matrix equation that looks like this : exp ( 7 C ) = ( A + B )-1 ( B-A ).
47.
The spectral domain method has one very important advantage over other strictly numerical-solutions to Maxwell's equations for FSS . And that is that it yields a matrix equation of very small dimensionality, so it is amenable to solution on virtually any type of computer.
48.
The dimension of these matrix equations is technically infinite, but by ignoring all contributions that correspond to an angular momentum quantum number l greater than { l _ { \ max } }, they have dimension { \ left ( + 1 } \ right ) ^ 2 }.
49.
Like the MFS and BEM, the SBM will produce dense coefficient matrices, whose operation count and the memory requirements for matrix equation buildup are of the order of " O " ( " N " 2 ) which is computationally too expensive to simulate large-scale problems.
50.
Other ways to optimize Dixon's method include using a better algorithm to solve the matrix equation, taking advantage of the sparsity of the matrix : a number " z " cannot have more than \ log _ 2 z factors, so each row of the matrix is almost all zeros.
