Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Published Research Papers (93)
- Asymptotic behavior (15)
- Conditional convergence (9)
- Toeplitz matrix (8)
- Asymptotic (6)
-
- Eigenvalue problem (6)
- Unpublished Papers (6)
- $(R (5)
- Free Textbooks and Supplements (5)
- Difference equations (4)
- Differential equations (4)
- Disconjugate (4)
- Inverse (4)
- Moore--Penrose inverse (4)
- Moore–Penrose inverse (4)
- Orthogonal polynomials (4)
- Smoothing (4)
- $R$-symmetric (3)
- Block circulant (3)
- Differential equation (3)
- Discrete Fourier transform (3)
- Eigenvalue (3)
- Eigenvalues (3)
- Expansion (3)
- Frobenius norm (3)
- Global (3)
- Moore--Penrose Inverse (3)
- Polynomial (3)
- Rationally generated (3)
- Schauder-Tychonoff theorem (3)
- Publication Year
- File Type
Articles 1 - 30 of 104
Full-Text Articles in Entire DC Network
Elementary Differential Equations With Boundary Value Problems, William F. Trench
Elementary Differential Equations With Boundary Value Problems, William F. Trench
William F. Trench
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some prepa- ration in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. …
Elementary Differential Equations, William F. Trench
Elementary Differential Equations, William F. Trench
William F. Trench
Elementary Differential Equations with Boundary Value Problems is written for students in science, engineering, and mathematics who have completed calculus through partial differentiation. If your syllabus includes Chapter 10 (Linear Systems of Differential Equations), your students should have some preparation in linear algebra. In writing this book I have been guided by the these principles: An elementary text should be written so the student can read it with comprehension without too much pain. I have tried to put myself in the student’s place, and have chosen to err on the side of too much detail rather than not enough. An …
Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench
Student Solutions Manual For Elementary Differential Equations And Elementary Differential Equations With Boundary Value Problems, William F. Trench
William F. Trench
No abstract provided.
Introduction To Real Analysis, William F. Trench
Introduction To Real Analysis, William F. Trench
William F. Trench
This is a text for a two-term course in introductory real analysis for junior or senior math- ematics majors and science students with a serious interest in mathematics. Prospective educators or mathematically gifted high school students can also benefit from the mathe- matical maturity that can be gained from an introductory real analysis course. The book is designed to fill the gaps left in the development of calculus as it is usually presented in an elementary course, and to provide the background required for insight into more advanced courses in pure and applied mathematics. The standard elementary calcu- lus sequence …
An Unnoticed Consequence Of Szego's Distribution Theorem, William F. Trench
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
Inverse Problems For Unilevel Block $\Alpha$-Circulants, William F. Trench
William F. Trench
No abstract provided.
Functions Defined By Improper Integrals, William F. Trench
Functions Defined By Improper Integrals, William F. Trench
William F. Trench
This is a supplement to the author's Introduction to Real Analysis. It has been judged to meet the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Textbook Initiative. It may be copied, modified, redistributed, translated, and built upon subject to the Creative Commons license
Attribution-NonCommercial-ShareAlike 3.0 Unported License.
A complete instructor's solution manual is available by email to wtrench@trinity.edu subject to verification of the requestor's faculty status.
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
Characterization And Properties Of $(R,S_\Sigma)$-Commutative Matrices, William F. Trench
William F. Trench
Let $R=P \diag(\gamma_{0}I_{m_{0}}, \gamma_{1}I_{m_{1}}, \dots, \gamma_{k-1}I_{m_{k-1}})P^{-1}\in\mathbb{C}^{m\times m}$ and $S_{\sigma}=Q\diag(\gamma_{\sigma(0)}I_{n_{0}},\gamma_{\sigma(1)}I_{n_{1}}, \dots,\gamma_{\sigma(k-1)}I_{n_{k-1}})Q^{-1}\in\mathbb{C}^{n\times n}$, where $m_{0}+m_{1}+\cdots +m_{k-1}=m$, $n_{0}+n_{1}+\cdots+n_{k-1}=n$, $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$ are distinct complex numbers, and $\sigma :\mathbb{Z}_{k}\to\mathbb{Z}_{k}= \{0,1, \dots, k-1\}$. We say that $A\in\mathbb{C}^{m\times n}$ is $(R,S_{\sigma})$-commutative if $RA=AS_{\sigma}$. We characterize the class of $(R,S_{\sigma})$-commutative matrrices and extend results obtained previously for the case where $\gamma_{\ell}=e^{2\pi i\ell/k}$ and $\sigma(\ell)=\alpha\ell+\mu \pmod{k}$, $0 \le \ell \le k-1$, with $\alpha$, $\mu\in\mathbb{Z}_{k}$. Our results are independent of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{k-1}$, so long as they are distinct; i.e., if $RA=AS_{\sigma}$ for some choice of $\gamma_{0}$, $\gamma_{1}$, \dots, $\gamma_{_{k-1}}$ (all distinct), then $RA=AS_{\sigma}$ for arbitrary of …
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
Asymptotic Preconditioning Of Linear Homogeneous Systems Of Differential Equations, William F. Trench
William F. Trench
No abstract provided.
The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench
The Relationship Between Trench's Toeplitz Inversion Algorithm And The Gohberg-Semencul Formula, William F. Trench
William F. Trench
No abstract provided.
Spectral Decomposition Of Kac-Murdock-Szego Matrices, William F. Trench
Spectral Decomposition Of Kac-Murdock-Szego Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
Characterization And Properties Of Matrices With $K$-Involutory Symmetries Ii, William F. Trench
William F. Trench
No abstract provided.
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
Properties Of Multilevel Block $\Alpha$-Circulants, William F. Trench
William F. Trench
No abstract provided.
Inverses Of Lower Triangular Toeplitz Matrices, William F. Trench
Inverses Of Lower Triangular Toeplitz Matrices, William F. Trench
William F. Trench
No abstract provided.
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
On Nonautonomous Linear Systems Of Differential And Difference Equations With $R$-Symmetric Coefficient Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench
Characterization And Properties Of Matrices With K-Involutory Symmetries, William F. Trench
William F. Trench
No abstract provided.
Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench
Absolute Equal Distribution Of The Eigenvalues Of Discrete Sturm-Liouville Problems, William F. Trench
William F. Trench
No abstract provided.
Functional Perturbations Of Nonoscillatory Second Order Difference Equations, William F. Trench
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
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.
On Matrices With Rotative Symmetries, William F. Trench
On Matrices With Rotative Symmetries, 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
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.
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
Multilevel Matrices With Involutory Symmetries And Skew Symmetries, William F. Trench
William F. Trench
No abstract provided.
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
Inverse Eigenproblems And Associated Approximation Problems For Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
William F. Trench
No abstract provided.
Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench
Hermitian, Hermitian R-Symmetric, And Hermitian R-Skew Symmetric Procrustes Problems, William F. Trench
William F. Trench
No abstract provided.
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, William F. Trench
Minimization Problems For (R,S)-Symmetric And (R,S)-Skew Symmetric Matrices, 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
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.
An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench
An Elementary Note On Asymptotic Properties Of Toeplitz And Multilevel Toeplitz Matrices, William F. Trench
William F. Trench
No abstract provided.
Characterization And Properties Of Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
Characterization And Properties Of Matrices With Generalized Symmetry Or Skew Symmetry, William F. Trench
William F. Trench
No abstract provided.
Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench
Spectral Distribution Of Hermitian Toeplitz Matrices Formally Generated By Rational Functions, William F. Trench
William F. Trench
No abstract provided.