Publications related to Polar Codes: Characterization of Exponent, Bounds, and Constructions

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

This work is concerned with the computation of the action of a matrix function f(A), such as the matrix exponential or the matrix square root, on a vector b. For a general matrix A, this can be done by computing the compression of A onto a suitable Krylov ...

Siam Publications2024

Preconditioning techniques for generalized Sylvester matrix equations

Yannis Dirk Voet

Sylvester matrix equations are ubiquitous in scientific computing. However, few solution techniques exist for their generalized multiterm version, as they recently arose in stochastic Galerkin finite element discretizations and isogeometric analysis. In th ...

2023

Iterative refinement of Schur decompositions

Daniel Kressner, Zvonimir Bujanovic

The Schur decomposition of a square matrix A is an important intermediate step of state-of-the-art numerical algorithms for addressing eigenvalue problems, matrix functions, and matrix equations. This work is concerned with the following task: Compute a (m ...

SPRINGER2022

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

Daniel Kressner, Ulf David Persson, Alice Cortinovis

This paper is concerned with two improved variants of the Hutch++ algorithm for estimating the trace of a square matrix, implicitly given through matrix-vector products. Hutch++ combines randomized low-rank approximation in a first phase with stochastic tr ...

SIAM PUBLICATIONS2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

Florence Graezer Bideau, Huishu Deng

Mega-events have been considered as a strategy to boost urban development, which shifts targets from expansion outside of the original city fabric to reuse of heritage. The bidirectional dynamic between mega-events and heritage has been emphasized, as the ...

2022

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a k x k submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix can a ...

ELSEVIER SCIENCE INC2020

Method of displaying an image on a see-through display

Sabine Süsstrunk, Adrien Birbaumer, Martinus Bosch

The present invention concerns a method of displaying an image on a see-through display. The method comprises: obtaining (101) a first electromagnetic radiation matrix of an object, the first matrix comprising first matrix elements representing radiation i ...

2019

Near-Optimal Finite-Length Scaling for Polar Codes Over Large Alphabets

Rüdiger Urbanke, Henry Pfister

For any prime power q, Mori and Tanaka introduced a family of q-ary polar codes based on the q x q Reed-Solomon polarization kernels. For transmission over a q-ary erasure channel, they also derived a closed-form recursion for the erasure probability of ea ...

2019

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Daniel Kressner, Stefano Massei, Alice Cortinovis

The problem of finding a

k\times k

submatrix of maximum volume of a matrix A is of interest in a variety of applications. For example, it yields a quasi-best low-rank approximation constructed from the rows and columns of A. We show that such a submatrix ...

MATHICSE2019

Polar Codes: Characterization of Exponent, Bounds, and Constructions

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SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Preconditioning techniques for generalized Sylvester matrix equations

Iterative refinement of Schur decompositions

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Method of displaying an image on a see-through display

Near-Optimal Finite-Length Scaling for Polar Codes Over Large Alphabets

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

SPEEDING UP KRYLOV SUBSPACE METHODS FOR COMPUTING f(A)b VIA RANDOMIZATION

Iterative refinement of Schur decompositions

Preconditioning techniques for generalized Sylvester matrix equations

Mega Event Reinforced Industrial Heritage Transformation: A typological matrix between narratives and practices

IMPROVED VARIANTS OF THE HUTCH plus plus ALGORITHM FOR TRACE ESTIMATION

On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

MATHICSE Technical Report : On maximum volume submatrices and cross approximation for symmetric semidefinite and diagonally dominant matrices

Method of displaying an image on a see-through display

Near-Optimal Finite-Length Scaling for Polar Codes Over Large Alphabets