least squares

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least squares

(lēst skwārz),
A principle of estimation invented by Gauss in which the estimates of a set of parameters in a statistical model are the quantities that minimize the sum of squared differences between the observed values of the dependent variable and the values predicted by the model.

least squares

a method of regression analysis. The line on a graph that best summarizes the relationship between two variables is the one that ensures that there is the least value of the sum of the squares of the deviation between the fitted curve and each of the original data points.
References in periodicals archive ?
In addition, the subproblems are now nonlinear least squares problems in the factor matrices.
Where [lambda] = 1 the adaptive least squares problem are equivalent to the total least squares problem, i.
In this section, we demonstrate how to adapt the LSQR algorithm of Paige and Sanders [19] for solving the low-order least squares problem (3.
which is just the problem of determining the correct value [mu] for the Tikhonov least squares problem such that the discrepancy principle holds with equality.
The key to an efficient implementation is to update an orthogonal factorization of the coefficient matrix in the least squares problem (3.
This decomposition of the problem suggests that we search first for a solution of the reduced least squares problem, that is, determine a suitable size n, the matrices [V.
perpendicular to]]y and we have effectively removed the linear parameters and now need to solve a non-linear least squares problem to find [alpha].
2) is replaced by an upper triangular least squares problem, which can be solved immediately.
Variable projection leads to the nonlinear least squares problem (1.
In this case, an iterative method such as LSQR [30] is applied to the least squares problem,
This method amounts to truncating the singular value decomposition of the coefficient matrix A in such a way that the smallest singular values of A are discarded, and then solving the modified least squares problem.