Numerical Algorithms and High-Performance Computing - CADMOS Chair

Chair

Related publications (333)

Solving Rank-Structured Sylvester And Lyapunov Equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off-diagonal blocks. This comprises proble ...

SIAM PUBLICATIONS2018

MATHICSE Technical Report : Fast solvers for 2D fractional differential equations using rank structured matrices

Marco Mazza, Stefano Massei

We consider the discretization of time-space diffusion equations with fractional derivatives in space and either 1D or 2D spatial domains. The use of implicit Euler scheme in time and finite differences or finite elements in space, leads to a sequence of d ...

MATHICSE2018

MATHICSE Technical Report : Fast QR decomposition of HODLR matrices

Daniel Kressner, Ana Susnjara

The efficient and accurate QR decomposition for matrices with hierarchical low-rank structures, such as HODLR and hierarchical matrices, has been challenging. Existing structure-exploiting algorithms are prone to numerical instability as they proceed indi- ...

MATHICSE2018

MATHICSE Technical Report : A fast spectral divide-and-conquer method for banded matrices

Daniel Kressner, Ana Susnjara

Based on the spectral divide-and-conquer algorithm by Nakatsukasa and Higham [SIAM J. Sci. Comput., 35(3):A1325{A1349, 2013], we propose a new algorithm for computing all the eigenvalues and eigenvectors of a symmetric banded matrix. For this purpose, we c ...

MATHICSE2018

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

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We consider integer programming problems max {c^Tx : A x = b, l

Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik2018

Consider the problem of minimizing a convex differentiable function on the probability simplex, spectrahedron, or set of quantum density matrices. We prove that the expo-nentiated gradient method with Armijo line search always converges to the optimum, if ...

2018

We present a theoretical analysis of the CORSING (COmpRessed SolvING) method for the numerical approximation of partial differential equations based on compressed sensing. In particular, we show that the best s-term approximation of the weak solution of a ...

2018

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In this work we introduce a two-level preconditioner for the efficient solution of large scale saddlepoint linear systems arising from the finite element (FE) discretization of parametrized Stokes equations.The proposed preconditioner extends the Multi Spa ...

MATHICSE2018

MATHICSE Technical Report : Quasi-Toeplitz matrix arithmetic : a Matlab toolbox

Stefano Massei

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind

A = T(a) + E

where

T(a) = (aj-i)_{i,j\in \mathbb{Z}_{+}}

E = (e_{i,j})_{i,j\in\mathbb{Z}_{+}}

is compact and the norms

\| a\|_{\mathcal{W}} =\sum_{i\in\mathbb{Z}} |a|_j

and $|E|_{ ...

MATHICSE2018