# Algorithmic Description - Explore the Science & Experts | ideXlab

## Algorithmic Description

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### Leonardo Robol – One of the best experts on this subject based on the ideXlab platform.

• ##### quasi toeplitz matrix arithmetic a matlab toolbox
Numerical Algorithms, 2019
Co-Authors: Dario Andrea Bini, Stefano Massei, Leonardo Robol

Abstract:

A quasi-Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$
where $T(a)=(a_{j-i})_{i,j\in \mathbb Z^{+}}$
, $E=(e_{i,j})_{i,j\in \mathbb Z^{+}}$
is compact and the norms
$\|a\|_{_{\mathcal {W}}}={\sum }_{i\in \mathbb Z}|a_{i}|$
and $\|E\|_{2}$
are finite. These properties allow to approximate any QT matrix, within any given precision, by means of a finite number of parameters. QT matrices, equipped with the norm
$\|A\|_{_{\mathcal {Q}\mathcal {T}}}=\alpha {\|a\|}_{_{\mathcal {W}}}+\|E\|_{2}$
, for $\alpha = (1+\sqrt 5)/2$
, are a Banach algebra with the standard arithmetic operations. We provide an Algorithmic Description of these operations on the finite parametrization of QT matrices, and we develop a MATLAB toolbox implementing them in a transparent way. The toolbox is then extended to perform arithmetic operations on matrices of finite size that have a Toeplitz plus low-rank structure. This enables the development of algorithms for Toeplitz and quasi-Toeplitz matrices whose cost does not necessarily increase with the dimension of the problem. Some examples of applications to computing matrix functions and to solving matrix equations are presented, and confirm the effectiveness of the approach.

• ##### quasi toeplitz matrix arithmetic a matlab toolbox
arXiv: Numerical Analysis, 2018
Co-Authors: Dario Andrea Bini, Stefano Massei, Leonardo Robol

Abstract:

A Quasi Toeplitz (QT) matrix is a semi-infinite matrix of the kind $A=T(a)+E$ where $T(a)=(a_{j-i})_{i,j\in\mathbb Z^+}$, $E=(e_{i,j})_{i,j\in\mathbb Z^+}$ is compact and the norms $\lVert a\rVert_{\mathcal W} = \sum_{i\in\mathbb Z}|a_i|$ and $\lVert E \rVert_2$ are finite. These properties allow to approximate any QT-matrix, within any given precision, by means of a finite number of parameters.
QT-matrices, equipped with the norm $\lVert A \rVert_{\mathcal QT}=\alpha\lVert a\rVert_{\mathcal{W}} \lVert E \rVert_2$, for $\alpha\ge (1+\sqrt 5)/2$, are a Banach algebra with the standard arithmetic operations. We provide an Algorithmic Description of these operations on the finite parametrization of QT-matrices, and we develop a MATLAB toolbox implementing them in a transparent way. The toolbox is then extended to perform arithmetic operations on matrices of finite size that have a Toeplitz plus low-rank structure. This enables the development of algorithms for Toeplitz and quasi-Toeplitz matrices whose cost does not necessarily increase with the dimension of the problem.
Some examples of applications to computing matrix functions and to solving matrix equations are presented, and confirm the effectiveness of the approach.

### Martin V. Butz – One of the best experts on this subject based on the ideXlab platform.

• ##### An AlgorithmicDescription of XCS
, 2002
Co-Authors: Martin V. Butz, Stewart W. Wilson

Abstract:

A concise Description of the XCS classifier system’s parameters, structures, and algorithms is presented as an aid to research. The algorithms are written in modularly structured pseudo code with accompanying explanations.

• ##### an AlgorithmicDescription of xcs
Lecture Notes in Computer Science, 2001
Co-Authors: Martin V. Butz, Wolfgang Stolzmann

Abstract:

The various modifications and extensions of the anticipatory classifier system (ACS) recently led to the introduction of ACS2, an enhanced and modified version of ACS. This chapter provides an overview over the system including all parameters as well as framework, structure, and environmental interaction. Moreover, a precise Description of all algorithms in ACS2 is provided.

• ##### an AlgorithmicDescription of acs2
IWLCS '00 Revised Papers from the Third International Workshop on Advances in Learning Classifier Systems, 2000
Co-Authors: Martin V. Butz, Wolfgang Stolzmann

Abstract:

The various modifications and extensions of the anticipatory classifier system (ACS) recently led to the introduction of ACS2, an enhanced and modified version of ACS. This chapter provides an overview over the system including all parameters as well as framework, structure, and environmental interaction. Moreover, a precise Description of all algorithms in ACS2 is provided.

### Wolfgang Stolzmann – One of the best experts on this subject based on the ideXlab platform.

• ##### an AlgorithmicDescription of xcs
Lecture Notes in Computer Science, 2001
Co-Authors: Martin V. Butz, Wolfgang Stolzmann

Abstract:

The various modifications and extensions of the anticipatory classifier system (ACS) recently led to the introduction of ACS2, an enhanced and modified version of ACS. This chapter provides an overview over the system including all parameters as well as framework, structure, and environmental interaction. Moreover, a precise Description of all algorithms in ACS2 is provided.

• ##### an AlgorithmicDescription of acs2
IWLCS '00 Revised Papers from the Third International Workshop on Advances in Learning Classifier Systems, 2000
Co-Authors: Martin V. Butz, Wolfgang Stolzmann

Abstract:

The various modifications and extensions of the anticipatory classifier system (ACS) recently led to the introduction of ACS2, an enhanced and modified version of ACS. This chapter provides an overview over the system including all parameters as well as framework, structure, and environmental interaction. Moreover, a precise Description of all algorithms in ACS2 is provided.

• ##### IWLCS – An AlgorithmicDescription of ACS2
, 2000
Co-Authors: Martin V. Butz, Wolfgang Stolzmann

Abstract:

The various modifications and extensions of the anticipatory classifier system (ACS) recently led to the introduction of ACS2, an enhanced and modified version of ACS. This chapter provides an overview over the system including all parameters as well as framework, structure, and environmental interaction. Moreover, a precise Description of all algorithms in ACS2 is provided.