Robert E. Hartwig

Works (26)

Updated: December 6th, 2023 05:01

2023 journal article

Divisibility of Finite Geometric Series

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, 46(5).

By: R. Hartwig* & P. Patricio *

author keywords: Finite geometric series; Divisibility; Greatest common divisor
topics (OpenAlex): Advanced Differential Equations and Dynamical Systems; Meromorphic and Entire Functions; Algebraic Geometry and Number Theory
Source: Web Of Science
Added: August 21, 2023

2023 journal article

The GCD for finite geometric series

FILOMAT, 37(29), 9973–9979.

By: R. Hartwig n & P. Patricio *

author keywords: Finite geometric series; Greatest common divisor
topics (OpenAlex): Digital Image Processing Techniques; Cryptography and Residue Arithmetic
Source: Web Of Science
Added: December 4, 2023

2021 journal article

From Euclid to Corner Sums - a Trail of Telescoping Tricks

FILOMAT, 35(14), 4613–4636.

By: P. Patricio * & R. Hartwig n

author keywords: Telescoping Sum; Corner Sum; Polynomials; Recurrence Relation
topics (OpenAlex): Polynomial and algebraic computation; Matrix Theory and Algorithms
Source: Web Of Science
Added: February 7, 2022

2018 journal article

PERTURBATION RESULTS AND THE FORWARD ORDER LAW FOR THE MOORE-PENROSE INVERSE OF A PRODUCT

ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 34, 514–525.

By: N. Castro-Gonzalez & R. Hartwig

topics (OpenAlex):
Source: NC State University Libraries
Added: December 3, 2018

2018 journal article

The group inverse of the nivellateur

LINEAR & MULTILINEAR ALGEBRA, 66(12), 2409–2420.

By: R. Hartwig* & P. Patricio *

author keywords: Nivellateur; group inverse; matrices over a field
topics (OpenAlex): Matrix Theory and Algorithms; Iterative Methods for Nonlinear Equations; Control Systems and Identification
Source: Web Of Science
Added: October 16, 2018

2015 journal article

Some regular sums

LINEAR & MULTILINEAR ALGEBRA, 63(1), 185–200.

By: P. Patricio * & R. Hartwig n

author keywords: 16E50; 15A09; Pierce decomposition; group inverse; reflexive inverses; outer inverses; block matrices; inverse
topics (OpenAlex): Matrix Theory and Algorithms; Finite Group Theory Research; Rings, Modules, and Algebras
Source: Web Of Science
Added: August 6, 2018

2014 journal article

Two by two units

Electronic Journal of Linear Algebra, 27, 489–503.

By: R. Hartwig n & P. Patricio *

topics (OpenAlex): Matrix Theory and Algorithms; graph theory and CDMA systems; Mathematical Analysis and Transform Methods
Source: NC State University Libraries
Added: August 6, 2018

2012 journal article

A note on power bounded matrices

Electronic Journal of Linear Algebra, 23, 625–645.

By: R. Hartwig n & P. Patricio *

topics (OpenAlex): Matrix Theory and Algorithms
Source: NC State University Libraries
Added: August 6, 2018

2010 journal article

THE LINK BETWEEN REGULARITY AND STRONG-PI-REGULARITY

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 89(1), 17–22.

By: P. Patricio * & R. Hartwig n

author keywords: Drazin inverse; strongly pi-regular; Drazin index
topics (OpenAlex): Rings, Modules, and Algebras; Advanced Topics in Algebra; Advanced Algebra and Logic
Source: Web Of Science
Added: August 6, 2018

2010 journal article

The (2,2,0) group inverse problem

APPLIED MATHEMATICS AND COMPUTATION, 217(2), 516–520.

By: P. Patricio * & R. Hartwig*

author keywords: Group inverse; Block matrices
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Topics in Algebra; Algebraic and Geometric Analysis
TL;DR: The existence of the group inverse of a two by two matrix with zero (2, 2) entry, over a ring is characterized by means of the existence of a suitable function of the other three entries. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2009 journal article

Some additive results on Drazin inverses

Applied Mathematics and Computation, 215(2), 530–538.

By: P. Patricio* & R. Hartwig*

topics (OpenAlex): Matrix Theory and Algorithms; Electromagnetic Scattering and Analysis; Numerical methods in inverse problems
TL;DR: Some additive results on Drazin inverse of a sum of Dazin invertible elements are derived and some converse results are presented. (via Semantic Scholar)
Source: NC State University Libraries
Added: August 6, 2018

2007 journal article

On Roth's pseudo equivalence over rings

Electronic Journal of Linear Algebra, 16, 111–124.

By: R. Hartwig n & P. Patricio *

topics (OpenAlex): Advanced Topics in Algebra; Matrix Theory and Algorithms; Rings, Modules, and Algebras
Source: NC State University Libraries
Added: August 6, 2018

2006 journal article

Note on a linear difference equation

AMERICAN MATHEMATICAL MONTHLY, 113(3), 250–256.

By: R. Hartwig*

topics (OpenAlex): Mathematical and Theoretical Epidemiology and Ecology Models; advanced mathematical theories; Opinion Dynamics and Social Influence
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
4. Quality Education (Web of Science)
Source: Web Of Science
Added: August 6, 2018

2006 journal article

The Picard iteration and its application

LINEAR & MULTILINEAR ALGEBRA, 54(5), 329–341.

By: X. Chen* & R. Hartwig n

author keywords: Picard iteration; Schur complement; path condition
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Topics in Algebra; Mathematics and Applications
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Diagonalizing triangular matrices via orthogonal Pierce decompositions

LINEAR ALGEBRA AND ITS APPLICATIONS, 401, 381–391.

By: R. Hartwig n, P. Patricio * & R. Puystjens*

author keywords: rings; triangular matrices; von Neumann regularity; diagonalization
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Topics in Algebra; Polynomial and algebraic computation
Source: Web Of Science
Added: August 6, 2018

2005 journal article

Focal power

Electronic Journal of Linear Algebra, 13, 56–71.

By: R. Hartwig n & J. Maroulas*

topics (OpenAlex):
UN Sustainable Development Goals Color Wheel
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Source: NC State University Libraries
Added: August 6, 2018

2005 journal article

Representations for the Drazin inverse of a 2 x 2 block matrix

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 27(3), 757–771.

By: R. Hartwig*, X. Li* & Y. Wei *

author keywords: index; Drazin inverse; generalized Schur complement; weighted Drazin inverse
topics (OpenAlex): Matrix Theory and Algorithms; Liquid Crystal Research Advancements; Electromagnetic Scattering and Analysis
TL;DR: Two representations for the Drazin inverse of a $2\times2$ block matrix M, where $A$ and $D$ are square matrices, are extended to the case where $C(I-AA^{D})=0$ and $(I- AA^{D)B=0) and the upper bounds for the index of $M$ are studied. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2005 journal article

The semi-iterative method applied to the hyper-power iteration

NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS, 12(9), 895–910.

By: X. Chen* & R. Hartwig n

author keywords: hyper-power iteration; semi-iterative method; asymptotic convergence rate; quotient convergence rate; root-convergence rate
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Optimization Algorithms Research; Iterative Methods for Nonlinear Equations
TL;DR: The semi-iterative method (SIM) is applied to the hyper-power (HP) iteration, and necessary and sufficient conditions are given for the convergence of the semi- iterative–hyper- power (SIM– HP) iteration. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

2004 journal article

Determinantal identities over commutative semirings

LINEAR ALGEBRA AND ITS APPLICATIONS, 387, 99–132.

By: P. Poplin* & R. Hartwig n

author keywords: semiring; determinant; laplace; Cauchy-Binet
topics (OpenAlex): Advanced Topics in Algebra; Matrix Theory and Algorithms; Polynomial and algebraic computation
Source: Web Of Science
Added: August 6, 2018

2001 journal article

Some additive results on Drazin inverse

LINEAR ALGEBRA AND ITS APPLICATIONS, 322(1-3), 207–217.

By: R. Hartwig n, G. Wang n & Y. Wei*

author keywords: Drazin inverse; additive results; perturbation
topics (OpenAlex): Matrix Theory and Algorithms; Stability and Control of Uncertain Systems; Advanced Optimization Algorithms Research
Source: Web Of Science
Added: August 6, 2018

2000 journal article

Creation and annihilation in matrix theory

LINEAR ALGEBRA AND ITS APPLICATIONS, 305(1-3), 47–65.

By: R. Hartwig n & K. Prasad *

author keywords: elimination; completion; adjoints; Brahma; Shiva
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Topics in Algebra; Molecular spectroscopy and chirality
Source: Web Of Science
Added: August 6, 2018

1999 journal article

Constrained convergence

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 29(1), 177–195.

By: R. Hartwig* & P. Semrl

topics (OpenAlex): Computability, Logic, AI Algorithms
Source: Web Of Science
Added: August 6, 2018

1998 journal article

Power additivity and orthogonality

SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS, 20(1), 1–13.

By: R. Hartwig n & P. Semrl

author keywords: power additivity; rank additivity; orthogonality; Cochran's theorem
topics (OpenAlex): Matrix Theory and Algorithms; Advanced Optimization Algorithms Research; graph theory and CDMA systems
TL;DR: The relation between rank additivity and orthogonality is analyzed and the central role played by Cochran's theorem is illustrated and the properties of orthogonal and power-additive families are investigated. (via Semantic Scholar)
Source: Web Of Science
Added: August 6, 2018

1997 journal article

Generalized polynomial bases and the Bezoutian

LINEAR ALGEBRA AND ITS APPLICATIONS, 251, 293–320.

By: V. Mani* & R. Hartwig n

topics (OpenAlex): Coding theory and cryptography; Polynomial and algebraic computation; graph theory and CDMA systems
Source: Web Of Science
Added: August 6, 2018

1997 journal article

On products of EP matrices

LINEAR ALGEBRA AND ITS APPLICATIONS, 252, 339–345.

By: R. Hartwig n & I. Katz*

topics (OpenAlex): Matrix Theory and Algorithms; Electromagnetic Scattering and Analysis; Electromagnetic Simulation and Numerical Methods
Source: Web Of Science
Added: August 6, 2018

1997 journal article

On the convergence of power scaled Cesaro sums

LINEAR ALGEBRA AND ITS APPLICATIONS, 267, 335–358.

By: X. Chen n & R. Hartwig n

topics (OpenAlex): Matrix Theory and Algorithms; Mathematical Inequalities and Applications; Advanced Mathematical Theories and Applications
Source: Web Of Science
Added: August 6, 2018

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