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Showing 1 to 12 of 12 for “"Toeplitz matrix"”.
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High-performance algorithms to solve Toeplitz and block Toeplitz matrices
Fast algorithms to factor Toeplitz matrices have existed since the beginning of this century. The two most notable algorithms to factor Toeplitz matrices are the Schur and the Levinson-Durbin. The former factors the Toeolitz matrix itself while the latter factors the inverse. In this thesis, we …
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A fast characteristic finite difference method for fractional advection-diffusion equations with non-linear reaction.
… the advection-diffusion equation utilizing fast Toeplitz matrix-vector multiplication. We then extend the method to the two-dimensional case. Numerical results are provided to compare performance of the methods proposed.
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A fast 3D full-wave solver for nanophotonics
… and solve a linear system. Moreover, the block Toeplitz matrix property and using FFT helps reduce memory requirement, and accelerate the circulant matrix vector product. Numerical experiments are presented to demonstrate that this method can effectively reduce reflections to 1%, and is easily …
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Structured linear algebra problems and applications to system identification
… of the broad class of positive definite Toeplitz-like matrices is given. For nearly semidefinite Toeplitz matrices, it is proven that the Cholesky factor has a limited rank-revealing property. This property has a close connection with a stability result for the Schur algorithm for the …
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Electromagnetic scattering and induction models for spheroidal geometries
… and computational complexity, the Sparse Matrix/Canonical Grid (SMCG) method is applied to 3-D dense media scattering. By approximating the dyadic Green's function about a canonical rectilinear grid, weak interaction between spheroid far apart may be quickly approximated. Strong …
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Biologically inspired feature extraction for rotation and scale tolerant pattern analysis
… model characterized by Topelitz-Block-Toeplitz matrix, the overall network response is obtained without matrix inverse operations providing the connection matrix generating function is bound by unity. It was shown that for the network with the inter-neuron connection function expandable …
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Isospectral algorithms, Toeplitz matrices and orthogonal polynomials
… isospectral algorithm is one which manipulates a matrix without changing its spectrum. In this thesis we study three interrelated examples of isospectral algorithms, all pertaining to Toeplitz matrices in some fashion, and one directly involving orthogonal polynomials. The first set of algorithms …
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Synthesis of ion microbeam column.
… and one upon the Levinson algorithm. for Toeplitz matrix inversion, are developed to complement the charge-density method in analyzing the new column structures. Various optimization schemes are combined to avoid shallow minima at a reasonable computational cost. With each plate …
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Robust communication in a time-varying noisy environment
… associated with the smallest eigenvalue of the Toeplitz matrix formed from the noise autocorrelation sequence. If the noise autocorrelation is not known in advance of transmission, or not stationary, then it must be estimated at the receiver. Since autocorrelation estimators derive their …
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Sampling in band-limited and shift-invariant spaces
Sampling and reconstruction of signals is an important topic in mathematical signal processing. The introduction of frames into such problems gives new interpretation of this area. Many new and eA?ective algorithms are based on this new approach. In this work, the theory of the frame-based …
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Methods of fast Fourier transform in diffraction problems of elastic and acoustic waves with applications to crack mechanics
… may be reduced to linear algebraic systems with matrix of Toepliz or circulant form. For both the types there can be applied fast iteration methods founded on Conjugate Gradient method with a preconditioning. This leads to a quasi-linear numerical algorithm. 2) Applications are constructed in …
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A Multigrid Acceleration for an ADI Finite Difference Method for Two-Dimensional Space Fractional Diffusion Equations
<p>Fractional diffusion equations are generalizations of classical diffusion equations which are used in modeling practical superdiffusive problems in fluid flow, finance and others. Because of the nonlocal property of fractional differential operators, the numerical methods for fractional …