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Articles 1 - 30 of 44

Full-Text Articles in Physical Sciences and Mathematics

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench Nov 2014

An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench

William F. Trench

No abstract provided.


Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench Feb 2013

Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench

William F. Trench

No abstract provided.


Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench Dec 2011

Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench Dec 2010

Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench Dec 2005

Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench

William F. Trench

No abstract provided.


Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench Dec 2004

Characterization And Properties Of $(R,S)$-Symmetric, $(R,S)$-Skew Symmetric, And $(R,S)$-Conjugate Matrices, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench Dec 2004

Asymptotic Relationships Between Singular Values Of Structured Matrices Similarly Generated By Different Formal Expansions Of A Rational Function, William F. Trench

William F. Trench

No abstract provided.


Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench Dec 2003

Simplification And Strengthening Of Weyl's Definition Of Asymptotic Equal Distribution Of Two Families Of Finite Sets, William F. Trench

William F. Trench

No abstract provided.


Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench Dec 2002

Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench

William F. Trench

No abstract provided.


Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench Dec 2001

Asymptotically Constant Solutions Of Functional Difference Systems, William F. Trench

William F. Trench

No abstract provided.


Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench Dec 1999

Systems Of Difference Equations With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.


Conditional Convergence Of Infinite Products, William F. Trench Dec 1998

Conditional Convergence Of Infinite Products, William F. Trench

William F. Trench

No abstract provided.


Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench Dec 1998

Linear Asymptotic Equilibrium For Nilpotent Systems Of Difference Equations, William F. Trench

William F. Trench

No abstract provided.


Trench's Canonical Form For A Disconjugate $N$Th-Order Linear Difference Equation, William F. Trench, Bennette Harris, Robert Krueger Dec 1997

Trench's Canonical Form For A Disconjugate $N$Th-Order Linear Difference Equation, William F. Trench, Bennette Harris, Robert Krueger

William F. Trench

No abstract provided.


Numerical Solution Of The Inverse Eigenvalue Problem For Real Symmetric Toeplitz Matrices, William F. Trench Dec 1996

Numerical Solution Of The Inverse Eigenvalue Problem For Real Symmetric Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench Dec 1992

A Note On Computing Eigenvalues Of Banded Hermitian Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


Global Solutions Of Nonlinear Differential Equations, William F. Trench Dec 1991

Global Solutions Of Nonlinear Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Behavior Of Solutions Of Functionally Perturbed Nonoscillatory Second Order Differential Equations, William F. Trench Dec 1990

Asymptotic Behavior Of Solutions Of Functionally Perturbed Nonoscillatory Second Order Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Spectral Evolution Of A One-Parameter Extension Of A Real Symmetric Toeplitz Matrix, William F. Trench Dec 1989

Spectral Evolution Of A One-Parameter Extension Of A Real Symmetric Toeplitz Matrix, William F. Trench

William F. Trench

No abstract provided.


General Functional Differential Systems With Asymptotically Constant Solutions, William F. Trench Dec 1988

General Functional Differential Systems With Asymptotically Constant Solutions, William F. Trench

William F. Trench

No abstract provided.


Existence Of Solutions Of Functional-Differential Systems With Prescribed Asymptotic Behavior, William F. Trench Dec 1988

Existence Of Solutions Of Functional-Differential Systems With Prescribed Asymptotic Behavior, William F. Trench

William F. Trench

No abstract provided.


Toeplitz Systems Associated With The Product Of A Formal Laurent Series And A Laurent Polynomial, William F. Trench Mar 1988

Toeplitz Systems Associated With The Product Of A Formal Laurent Series And A Laurent Polynomial, William F. Trench

William F. Trench

No abstract provided.


Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench Mar 1988

Numerical Solution Of The Eigenvalue Problem For Symmetric Rationally Generated Toeplitz Matrices, William F. Trench

William F. Trench

No abstract provided.


Asymptotic Integration Of A Perturbed Constant Coefficient Differential Equation Under Mild Integral Smallness Conditions, William F. Trench Feb 1988

Asymptotic Integration Of A Perturbed Constant Coefficient Differential Equation Under Mild Integral Smallness Conditions, William F. Trench

William F. Trench

No abstract provided.


Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench Dec 1987

Efficient Application Of The Schauder-Tychonoff Theorem To Functional Perturbations Of $X^(N)=0$, William F. Trench

William F. Trench

No abstract provided.


On The Eigenvalue Problem For A Class Of Band Matrices Including Those With Toeplitz Inverses, William F. Trench Dec 1985

On The Eigenvalue Problem For A Class Of Band Matrices Including Those With Toeplitz Inverses, William F. Trench

William F. Trench

No abstract provided.


Existence Of Global Solutions With Prescribed Asymptotic Behavior For Nonlinear Differential Equations, William F. Trench Dec 1984

Existence Of Global Solutions With Prescribed Asymptotic Behavior For Nonlinear Differential Equations, William F. Trench

William F. Trench

No abstract provided.


On The Eigenvalue Problem For Toeplitz Matrices Generated By Rational Functions, William F. Trench Dec 1984

On The Eigenvalue Problem For Toeplitz Matrices Generated By Rational Functions, William F. Trench

William F. Trench

We give formulas for the characteristic polynomial and eigenvectors of of $n\times n$ Toeplitz matrices generated by a formal Laurent series of a rational function $R(z)$. The formulas are in terms of a certain fixed polynomial with coefficients that are simple functions of $\lambda$ and the coefficients of $R(z)$. The complexity of the formulas is independent of $n$.


Functional Perturbations Of Second Order Differential Equations, William F. Trench Dec 1984

Functional Perturbations Of Second Order Differential Equations, William F. Trench

William F. Trench

No abstract provided.


Explicit Inversion Formulas For Toeplitz Band Matrices, William F. Trench Dec 1984

Explicit Inversion Formulas For Toeplitz Band Matrices, William F. Trench

William F. Trench

No abstract provided.