Sentence examples for least squared problem from inspiring English sources

Solve the least squared problem to obtain the reconstructed signal, z t. z t = arg min z y - Φ t z 2. Calculate the new approximation, a t, that best describes y.

(d) Solve the least squared problem to obtain the reconstructed signal, z t. z t = arg min z y - Φ t z 2   (e) Calculate the new approximation, a t, that best describes y.

(d) Solve the following least squared problem to obtain the new reconstructed signal, z t. z t = arg min z y - Φ t z 2   (e) Calculate the new approximation, a t, that best describes y.

Solve the following least squared problem to obtain the new reconstructed signal, z t. z t = arg min z y - Φ t z 2. Calculate the new approximation, a t, that best describes y.

Solve the least squared problem to obtain the new reconstructed signal, z t. z t = arg min z y - Φ t z 2. Calculate the new approximation, a t, and find the residual (error, r t ). a t is the projection of y on the space spanned by Φ t. a t = Φ t z t r t = y - a t.

(b) Solve the least squared problem to obtain the new reconstructed signal, z t. z t = arg min z y - Φ t z 2   (c) Calculate the new approximation, a t, and find the residual (error, r t ). a t is the projection of y on the space spanned by Φ t. a t = Φ t z t r t = y - a t.  .

Now, by means of the SVD we solve the Total Least Squares problem of finding both the reference kernels and the interpolation functions that minimize, for a given number J of reference kernels, the mean squared error (MSE) of the linear combination [15]: K = U K S K V K T = ∑ r = 1 R u r s r v r T ≃ ∑ r = 1 J u r s r v r T, (8).

Since is not a square matrix, to solve (3), one constructs a least-squares problem which finds that minimizes the squared error [7], (4).

By subtracting the squared distance of the first RO from the squared distances of the remaining ROs, a linear least-squares problem with solution p ^ = S T W ′ S - 1 S T W ′ b (49). is obtained, in which S = x 2 - x 1 y 2 - y 1 x 3 - x 1 y 3 - y 1 ⋮ ⋮ x B - x 1 y B - y 1 (50).

We review essential theory for ridge approximation – e.g., the best mean-squared approximation and an optimal low-dimensional subspace – and we prove that the gradient-based active subspace is near-stationary for the least-squares problem that defines an optimal subspace.

A minimization problem using the least squared error (i.e., difference) between the eigenvector and target mode shape is set as a sample objective function for both the first and second eigenmodes.