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The essential dimension is a numerical invariant of the group; it is often equal to the minimal number of independent parameters required to describe all algebraic objects of a certain type.
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We do this in a setting that closely resembles the numerical analysis setting of Mallat and Zhong and that seems to capture something of the essence of their (practical) reconstruction method.
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We do this in a setting that closely resembles the numerical analysis setting of Mallat and Zhong and that seems to capture something of the essence of their (practical) reconstruction method.
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Mathematical details and numerical examples are included.
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Then, we describe a numerical method to compute the dual function and give an estimate of the error.
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Singular Value Estimates for Certain Convolution-Product Operators
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We present two-sided singular value estimates for a class of convolution-product operators related to time-frequency localization.
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Singular Value Estimates for Certain Convolution-Product Operators
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The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems.
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We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space.
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Numeric simulation for structure's damage identification of space truss
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Different classes of logical determinants-numeric characteristics of matrices that can be expressed through the operations of the continuous logic-are studied.
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Numeric values are introduced to measure the discrepancy between the trees.
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The calculations were performed in Maple V R5 with the use of the standard subroutine dsolve/numeric for solving ordinary differential equations by the fourth-order Runge-Kutta method.
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To ensure the convergence of the iterative process implemented in the Numeric package in REDUCE, proper initial data must be specified.
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It is well known that Gabor expansions generated by a lattice of Nyquist density are numerically unstable, in the sense that they do not constitute frame decompositions.
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Spherical harmonic series have many of the same wonderful properties as Fourier series, but have lacked one important thing: a numerically stable fast transform analogous to the Fast Fourier Transform (FFT).
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Finally, we consider the spline of order 2; we investigate numerically the region of the time-frequency plane where it generates a frame and we compute the dual function for some values of the parameters.
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This makes them numerically attractive for applications in geophysical modeling.
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It is simple in structure, implementable, numerically efficient and has global convergence.
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