A stable method to model the acoustic response of multilayered
... is of infinite extent in the lateral directions and the structure is excited by an incident monochromatic plane wave. Basically, the method consists in decomposing the wave fields in each layer into forward and backward waves and in applying the boundary conditions at each layer interfaces. This met ...
... is of infinite extent in the lateral directions and the structure is excited by an incident monochromatic plane wave. Basically, the method consists in decomposing the wave fields in each layer into forward and backward waves and in applying the boundary conditions at each layer interfaces. This met ...
3 Best-Fit Subspaces and Singular Value Decompo
... Think of the rows of an n × d matrix A as n data points in a d-dimensional space and consider the problem of finding the best k-dimensional subspace with respect to the set of points. Here best means minimize the sum of the squares of the perpendicular distances of the points to the subspace. We beg ...
... Think of the rows of an n × d matrix A as n data points in a d-dimensional space and consider the problem of finding the best k-dimensional subspace with respect to the set of points. Here best means minimize the sum of the squares of the perpendicular distances of the points to the subspace. We beg ...
The Three Point Pick Problem on the Bidisk
... geodesic disk passing through 1 and 2 , but will not be unique o this disk. (For the example 1 = (0 0) 2 = ( 12 12 ) w1 = 0 w2 = 21 , on the diagonal f(z z )g we must have (z z ) = z but o the diagonal any convex combination of the two coordinate functions z 1 and z 2 will work). It ...
... geodesic disk passing through 1 and 2 , but will not be unique o this disk. (For the example 1 = (0 0) 2 = ( 12 12 ) w1 = 0 w2 = 21 , on the diagonal f(z z )g we must have (z z ) = z but o the diagonal any convex combination of the two coordinate functions z 1 and z 2 will work). It ...
Blue Exam
... Solution: The first three columns, call these vectors x1 , x2 , x3 respectively, of A form a basis for col(A). We apply the Gram-Schmidt Process to these to obtain an orthogonal basis {v1 , v2 , v3 } for col(A). ...
... Solution: The first three columns, call these vectors x1 , x2 , x3 respectively, of A form a basis for col(A). We apply the Gram-Schmidt Process to these to obtain an orthogonal basis {v1 , v2 , v3 } for col(A). ...
8 Finite-difference methods for BVPs
... Note that the problem we need to handle for such a generalization is obtaining an approximation to y 0 (a) in (8.31) that would have the accuracy consistent with the accuracy of the discretization scheme. That is, the accuracy needs to be second-order for a generalization of (8.4) and fourthorder fo ...
... Note that the problem we need to handle for such a generalization is obtaining an approximation to y 0 (a) in (8.31) that would have the accuracy consistent with the accuracy of the discretization scheme. That is, the accuracy needs to be second-order for a generalization of (8.4) and fourthorder fo ...
Local Loss Optimization in Operator Models: A New Insight
... learning observable operators from a loss minimization perspective. In particular, we give a formulation of the problem in terms of a regularized local loss minimization. We emphasize the local aspect of this minimization – which means that, in order to learn a function computed by an operator model ...
... learning observable operators from a loss minimization perspective. In particular, we give a formulation of the problem in terms of a regularized local loss minimization. We emphasize the local aspect of this minimization – which means that, in order to learn a function computed by an operator model ...
On Importance Sampling for State Space Models
... a device of simulating the state vector α based on a simulated signal vector, both conditional on y. The methods are implemented for a stochastic volatility model with leverage. The new modifications are necessary for the maximum likelihood estimation of parameters and the signal extraction of funct ...
... a device of simulating the state vector α based on a simulated signal vector, both conditional on y. The methods are implemented for a stochastic volatility model with leverage. The new modifications are necessary for the maximum likelihood estimation of parameters and the signal extraction of funct ...
Proposition 2 - University of Bristol
... sufficient. Nevertheless, Proposition 2 is useful and important in practice. When creating a covariance matrix it is natural to want to choose specific values for the partial correlations, and Proposition 2 places strong restrictions on what these can be. Proposition 2 has several other interesting ...
... sufficient. Nevertheless, Proposition 2 is useful and important in practice. When creating a covariance matrix it is natural to want to choose specific values for the partial correlations, and Proposition 2 places strong restrictions on what these can be. Proposition 2 has several other interesting ...
On Importance Sampling for State Space Models
... a device of simulating the state vector α based on a simulated signal vector, both conditional on y. The methods are implemented for a stochastic volatility model with leverage. The new modifications are necessary for the maximum likelihood estimation of parameters and the signal extraction of funct ...
... a device of simulating the state vector α based on a simulated signal vector, both conditional on y. The methods are implemented for a stochastic volatility model with leverage. The new modifications are necessary for the maximum likelihood estimation of parameters and the signal extraction of funct ...
Non-negative matrix factorization
NMF redirects here. For the bridge convention, see new minor forcing.Non-negative matrix factorization (NMF), also non-negative matrix approximation is a group of algorithms in multivariate analysis and linear algebra where a matrix V is factorized into (usually) two matrices W and H, with the property that all three matrices have no negative elements. This non-negativity makes the resulting matrices easier to inspect. Also, in applications such as processing of audio spectrograms non-negativity is inherent to the data being considered. Since the problem is not exactly solvable in general, it is commonly approximated numerically.NMF finds applications in such fields as computer vision, document clustering, chemometrics, audio signal processing and recommender systems.