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- Berkant Savas, Lars Eldén
- Pattern Recognition
- 2007

In this paper we present two algorithms for handwritten digit classification based on the higher order singular value decomposition (HOSVD). The first algorithm uses HOSVD for construction of the class models and achieves classification results with error rate lower than 6%. The second algorithm uses the HOSVD for tensor approximation simultaneously in two… (More)

- Lars Eldén
- Computational Statistics & Data Analysis
- 2004

- Lars Eldén, Haesun Park
- Numerische Mathematik
- 1999

An orthogonal Procrustes problem on the Stiefel manifold is studied , where a matrix Q with orthonormal columns is to be found that minimizes kAQ ? Bk F for an l m matrix A and an l n matrix B with l m and m > n. Based on the normal and secular equations and the properties of the Stiefel manifold, necessary conditions for a global minimum, as well as… (More)

- Lars Eldén, Berkant Savas
- SIAM J. Matrix Analysis Applications
- 2009

We derive a Newton method for computing the best rank-(r 1 , r 2 , r 3) approximation of a given J × K × L tensor A. The problem is formulated as an approximation problem on a product of Grassmann manifolds. Incorporating the manifold structure into Newton's method ensures that all iterates generated by the algorithm are points on the Grassmann manifolds.… (More)

- L. ELDÉN, P. C. HANSEN, M. ROJAS
- 2005

The minimization of linear functionals defined on the solutions of discrete ill-posed problems arises, e.g., in the computation of confidence intervals for these solutions. In 1990, Eldén proposed an algorithm for this minimization problem based on a para-metric programming reformulation involving the solution of a sequence of trust-region problems, and… (More)

- Lars Eldén
- 2003

- Lars Eldén, Fredrik Berntsson, Teresa Reginska
- SIAM J. Scientific Computing
- 2000

We consider an inverse heat conduction problem, the Sideways Heat Equation, which is a model of a problem, where one wants to determine the temperature on both sides of a thick wall, but where one side is inaccessible to measurements. Mathematically it is formulated as a Cauchy problem for the heat equation in a quarter plane, with data given along the line… (More)

- Eva Lundström, Lars Eldén
- SIAM J. Matrix Analysis Applications
- 2002

We consider the problem of updating an invariant subspace of a Hermitian, large and struc-tured matrix when the matrix is modiied slightly. The problem can be formulated as that of computing stationary values of a certain function, with orthogonality constraints. The constraint is formulated as the requirement that the solution must be on the Grassmann… (More)

- Hyunsoo Kim, Haesun Park, Lars Eldén
- BIBE
- 2007

— Non-negative matrix factorization (NMF) and non-negative tensor factorization (NTF) have attracted much attention and have been successfully applied to numerous data analysis problems where the components of the data are necessarily non-negative such as chemical concentrations in experimental results or pixels in digital images.

- Haesun Park, Lars Eldén
- SIAM J. Matrix Analysis Applications
- 1995