Publications related to Low Rank Updates for the Cholesky Decomposition

MATHICSE Technical Report : Bounds for the decay of the entries in inverses and Cauchy- Stieltjes functions of sparse, normal matrices

It is known that in many functions of banded, and more generally, sparse Hermitian positive definite matrices, the entries exhibit a rapid decay away from the sparsity pattern. This is in particular true for the inverse, and based on results for the invers ...

MATHICSE2017

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Daniel Kressner, Robert Gerhard Jérôme Luce

The computation of the matrix exponential is a ubiquitous operation in numerical mathematics, and for a general, unstructured n×n matrix it can be computed in O(n3) operations. An interesting problem arises if the input matrix is a Toeplitz matrix, for exa ...

MATHICSE2016

Parallel algorithms for tensor completion in the CP format

Daniel Kressner, André Uschmajew

Low-rank tensor completion addresses the task of filling in missing entries in multidimensional data. It has proven its versatility in numerous applications, including context aware recommender systems and multivariate function learning. To handle large-sc ...

Elsevier Science Bv2016

Randomized Single-View Algorithms for Low-Rank Matrix Approximation

Volkan Cevher, Alp Yurtsever

This paper develops a suite of algorithms for constructing low-rank approximations of an input matrix from a random linear image of the matrix, called a sketch. These methods can preserve structural properties of the input matrix, such as positive-semideni ...

Under review2016

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Michaël Unser, Julien René Pierre Fageot, Harshit Gupta

We present a theoretical analysis and comparison of the effect of

ℓ _{ 1 }

versus

ℓ _{ 2 }

regularization for the resolution of ill-posed linear inverse and/or compressed sensing problems. Our formulation covers the most general setting where the s ...

IEEE2016

A block algorithm for computing antitriangular factorizations of symmetric matrices

Daniel Kressner, Zvonimir Bujanovic

Any symmetric matrix can be reduced to antitriangular form in finitely many steps by orthogonal similarity transformations. This form reveals the inertia of the matrix and has found applications in, e.g., model predictive control and constraint preconditio ...

Springer2016

Programming with Numerical Uncertainties

Eva Darulova

Numerical software, common in scientific computing or embedded systems, inevitably uses an approximation of the real arithmetic in which most algorithms are designed. In many domains, roundoff errors are not the only source of inaccuracy and measurement as ...

EPFL2014

Evaluating functions of positive-definite matrices using colored-noise thermostats

Michele Ceriotti, Michele Parrinello

Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that scal ...

Amer Physical Soc2014

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Meiyue Shao

Small relative perturbations to the entries of an essentially nonnegative matrix introduce small relative errors to entries of its exponential. It is thus desirable to compute the exponential with high componentwise relative accuracy. Taylor series approxi ...

Siam Publications2014

Low-Rank Tensor Methods for Communicating Markov Processes

Daniel Kressner, Francisco Santos Paredes Quartin de Macedo

Stochastic models that describe interacting processes, such as stochastic automata networks, feature a dimensionality that grows exponentially with the number of processes. This state space explosion severely impairs the use of standard methods for the num ...

Springer-Verlag Berlin2014

Low Rank Updates for the Cholesky Decomposition

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MATHICSE Technical Report : Bounds for the decay of the entries in inverses and Cauchy- Stieltjes functions of sparse, normal matrices

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Parallel algorithms for tensor completion in the CP format

Randomized Single-View Algorithms for Low-Rank Matrix Approximation

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

A block algorithm for computing antitriangular factorizations of symmetric matrices

Programming with Numerical Uncertainties

Evaluating functions of positive-definite matrices using colored-noise thermostats

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Low-Rank Tensor Methods for Communicating Markov Processes

MATHICSE Technical Report : Bounds for the decay of the entries in inverses and Cauchy- Stieltjes functions of sparse, normal matrices

MATHICSE Technical Report : Fast computation of the matrix exponential for a Toeplitz matrix

Representer Theorems for Sparsity-Promoting $ ℓ _{ 1 } $ Regularization

Programming with Numerical Uncertainties

Low-Rank Tensor Methods for Communicating Markov Processes

Aggressively Truncated Taylor Series Method For Accurate Computation Of Exponentials Of Essentially Nonnegative Matrices

Randomized Single-View Algorithms for Low-Rank Matrix Approximation

Parallel algorithms for tensor completion in the CP format

A block algorithm for computing antitriangular factorizations of symmetric matrices

Evaluating functions of positive-definite matrices using colored-noise thermostats