Publications
Breaking the curse of dimensionality, or how to use SVD in many dimensions
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pdf (324KB)
pdf (324KB)
Details:
Submitted to Siam Journal on Scientific Computing
Keywords:
Curse of dimensionality; Canonical decomposition; Tucker decomposition; Tree-Tucker format
Categories:
Uncategorized
How to find a good submatrix
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pdf (140KB)
pdf (140KB)
Details:
A maxvol algorithm is described for the computation of the "most nonsingular submatrix". This submatrix plays a key role in low rank approximation.
Keywords:
Maximum volume; Low-rank approximations; Global optimization
Categories:
Uncategorized
Minimization methods for approximating tensors and their comparison
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pdf (230KB)
pdf (230KB)
Details:
Three standard optimization methods (ALS, Gauss-Newton and Levenberg-Marquadt) are applied to the problem of tensor approximation and are compared.
Keywords:
Tensor approximation, trilinear decomposition, PARAFAC
Categories:
Uncategorized
Linear algebra for tensor problems
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pdf (198KB)
pdf (198KB)
Details:
Submitted to Computing
Keywords:
Multidimensional arrays; Tucker decomposition; low rank approximations
Categories:
Uncategorized
Improved n-term Karatsuba-like formulae in GF(2)
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pdf (78KB)
pdf (78KB)
Details:
Submitted to IEEE Trans Computers
Keywords:
Optimal polynomial multiplication
Categories:
Uncategorized
Use of divided differences and B-splines for constructing fast discrete transforms of wavelet type on nonuniform grids
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pdf (166KB)
pdf (166KB)
Details:
Math. Notes, 2005(77), pp. 743-752
Keywords:
Wavelets
Categories:
Uncategorized
Fast simultaneous orthogonal reduction to triangular matrices
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pdf (188KB)
pdf (188KB)
Keywords:
Simultaneous reduction, diagonalization, Schur decomposition
Categories:
Uncategorized
Optimal Karatsuba-like formulae for certain bilinear forms in GF(2)
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pdf (142KB)
pdf (142KB)
Keywords:
Optimal algorithms, trilinear decomposition
Categories:
Uncategorized
Matrix-inversion cases with size-independent tensor rank estimates
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pdf (212KB)
pdf (212KB)
Keywords:
Tensor rank; Inverse matrices; Rank estimates
Categories:
Uncategorized
Superfast inversion of two-level Toeplitz matrices using Newton iteration and tensor-displacement structure
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pdf (141KB)
pdf (141KB)
Keywords:
Superfast algorithm, Newton iteration, approximate methods, Toeplitz matrices, displacement structure
Categories:
Uncategorized
Lower bounds for separable approximations of the Hilbert kernel
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pdf (198KB)
pdf (198KB)
Keywords:
Hilbert kernel, skeleton decomposition, lower bounds, Zolotarev function, elliptic functions
Categories:
Uncategorized
Integral operator with logarithmic kernel has only one positive eigenvalue
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pdf (105KB)
pdf (105KB)
Keywords:
Logarithmic kernel, positive eigenvalue
Categories:
Uncategorized
A unifying approach to the construction of circulant preconditioner
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pdf (225KB)
pdf (225KB)
Details:
Linear Algebra Appl
Keywords:
best circulant preconditioners, black dot algorithms, Toeplitz matrices
Categories:
Uncategorized
Tucker dimensionality reduction of three-dimensional arrays in linear time
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pdf (262KB)
pdf (262KB)
Keywords:
Tucker decomposition, skeleton decomposition, cross approximation, superfast algorithm, data compression
Categories:
Uncategorized
Tensor properties of multilevel Toeplitz and related matrices
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pdf (191KB)
pdf (191KB)
Keywords:
Multilevel matrices, Toeplitz matrices, tensor approximation, asymptotically smooth functions, fast inversion
Categories:
Uncategorized
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