Tom Bella Department of Mathematics University of Rhode Island

  • Office: Lippitt 101D
  • Email: tombella@uri.edu

  • All math placement inquiries: Click Here

Office Hours - Fall 2018

  • Mon 10am-12pm OR Wed 10am-12pm
    (varies by week)

Research Interests

  • Scientific computing and numerical linear algebra.
  • Matrix theory, structured matrices, matrices with quasiseparable structure.
  • Indefinite inner product spaces.
  • Signal processing and control theory.
  • Algebraic coding theory.

Awards

2017 College of Arts and Science Student Success Award - Awarded for "years of work to develop an effective in-house placement test for mathematics. Thanks to these efforts, there was a significant reduction in DFW grades and students were able to make more efficient and effective progress to graduation."

Publications

  • A QR algorithm for out-of-band quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), in preparation
  • Quasiseparable-Totally Nonnegative Matrices and Accurate Computations (with F. Dopico, V. Olshevsky), in preparation
  • Fast algorithms for multiplication of a quasiseparable matrix by a vector (with V. Olshevsky, M. Stewart), in preparation
  • Using unitary Hessenberg matrices to factor projectors (with V. Olshevsky, A. Phillips), in preparation
  • Classifications of three-term and two-term recurrence relations via subclasses of quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), submitted to SIAM Journal of Matrix Analysis (SIMAX)
  • The Spectral Connection Matrix for Any Change of Basis within the Classical Real Orthogonal Polynomials (with J. Reis), Mathematics, Special Issue New Trends in Applications of Orthogonal Polynomials and Special Functions, Mathematics 2015, 3, 382-397 (2015)
  • The spectral connection matrix for classical orthogonal polynomials of a single parameter (with J. Reis), Linear Algebra and Its Applications, Volume 458, 1 October 2014, Pages 161–182 (2014)
  • Nested Product Decomposition of a Quasiseparable Matrix (with V. Olshevsky, M. Stewart), SIAM. J. Matrix Anal. & Appl., 34(4), 1520–1555 (2013)
  • Fast inversion of polynomial-Vandermonde matrices for polynomial systems related to order one quasiseparable matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov), Advances in Structured Operator Theory and Related Areas, Operator Theory: Advances and Applications, Vol. 237, Pages 79-106 (referreed according to the standards of the Journal of Integral Equations and Operator Theory), Kaashoek, Marinus A.; Rodman, Leiba; Woerdeman, Hugo J. (Eds.) (2013)
  • Classifications of recurrence relations via subclasses of (H,k)-quasiseparable matrices (with V. Olshevsky, P. Zhlobich), Numerical Linear Algebra in Signals, Systems and Control, Lecture Notes in Electrical Engineering, Springer-Verlag, Lecture Notes in Electrical Engineering, Vol. 80, 1st Edition., 23-54 (2011)
  • A quasiseparable approach to five-diagonal CMV and companion matrices (with V. Olshevsky, P. Zhlobich), Linear Algebra and its Applications, Volume 434, Issue 4, 15 February 2011, Pages 957-976 (2011)
  • A Traub-like algorithm for Hessenberg-quasiseparable-Vandermonde matrices of arbitrary order (with Y. Eidelman, I. Gohberg, V. Olshevsky, E. Tyrtyshnikov, P. Zhlobich), Numerical methods for structured matrices and applications, 127–154, Operator Theory: Advances and Applications, 199, Birkhauser Verlag, Basel (2010)
  • Signal Flow Graph Approach to Inversion of (H,m)-Quasiseparable Vandermonde Matrices and New Filter Structures (with V. Olshevsky, P. Zhlobich), Linear Algebra and its Applications, Volume 432, Issue 8, 1 April 2010, Pages 2032-2051 (2010)
  • A fast Bjorck-Pereyra-type algorithm for solving Hessenberg-quasiseparable-Vandermonde systems (with Y. Eidelman, I. Gohberg, I. Koltracht, V. Olshevsky), SIAM. J. Matrix Anal. & Appl., Volume 31, Issue 2, pp. 790-815 (2009)
  • Computations with quasiseparable polynomials and matrices (with Y. Eidelman, I. Gohberg, V. Olshevsky), Theoretical Computer Science, Volume 409, Issue 2, 17 December 2008, Pages 158-179 (2008)
  • Lipschitz stability of canonical Jordan bases of H-selfadjoint matrices under structure-preserving perturbations (with V. Olshevsky, U. Prasad), Linear Algebra and its Applications, Volume 428, Issues 8-9, 15 April 2008, Pages 2130-2176 (2008)
  • Ranks of Hadamard Matrices and Equivalence of Sylvester Hadamard and Pseudo-Noise Matrices (with V. Olshevsky, L. Sakhnovich), Recent Advances in Matrix and Operator Theory, 35--46, Oper. Theory Adv. Appl., 179, Birkhauser, Basel, (An updated version containing new results of the conference proceedings in: Proc. SPIE Vol. 5910. in 2005) (2008)
  • A Bjorck-Pereyra-type algorithm for Szego-Vandermonde matrices based on properties of unitary Hessenberg matrices (with Y. Eidelman, I. Gohberg, I. Koltracht, V. Olshevsky), Linear Algebra and Applications, Volume 420, Issues 2-3 pp. 634-647 (2007)
  • Equivalence of Hadamard matrices and pseudo-noise matrices (with V. Olshevsky, L. Sakhnovich), Advanced Signal Processing Algorithms, Architectures, and Implementations XV, Proceedings of SPIE Volume: 5910, Franklin T. Luk, Editors, 59100V (2005)

Ph.D. Students

Jenna Reis, Ph.D. - University of Rhode Island, 2015 - Thesis: The spectral connection matrix for classical real orthogonal polynomials

Education

B.S. Mathematics - Adelphi University, 2003

B.S. Physics - Adelphi University, 2003

M.S. Mathematics - University of Connecticut, 2005

Ph.D. Mathematics - University of Connecticut, 2008 - Advisor: Vadim Olshevsky - Thesis: Topics in Numerical Linear Algebra related to Quasiseparable and Other Structured Matrices

Current Teaching

MTH 105 - Elementary Mathematical Codebreaking

MTH 215 - Introduction to Linear Algebra

MTH 215 Student Notes - Chapter 1
MTH 215 Student Notes - Chapter 2

Homework

Chapter 1
Section 1.1) 1-4, 7-13 odd, 15-25
Section 1.2) 1-5, 7-13 odd, 17-22, 25, 26, 28, 29
Section 1.3) 5, 6, 9-14, 21-25, 29, 30
Section 1.4) 1-7 odd, 11, 12, 17-26
Section 1.5) 1-11 odd, 23, 24, 26, 27
Section 1.6) 5-8
Section 1.7) 1-8, 11-19 odd, 21, 22, 27-29, 31-38
Section 1.8) 1-4, 9-12, 21-23
Section 1.9) 1-9 odd, 17-21 odd, 23, 24

Chapter 2
Section 2.1) 1, 2, 5-11, 15-22
Section 2.2) 1-11, 14-18, 21-23
Section 2.3) 1-8, 11-21, 31, 32
Section 2.4) 1-6, 11-13, 21
Section 2.5) 1-13 odd, 17-21
Section 2.6) 1-7, 9, 10

Chapter 3
Section 3.1) 1-12, 15, 17, 25-30

Chapter 4
Section 4.1) 1-11, 13-19 odd, 20-24
Section 4.2) 1-7, 9-19 odd, 25-27
Section 4.3) 1-10, 13-16, 19-24
Section 4.4) 1-10, 11, 13, 15-18
Section 4.5) 1-11 odd, 19-23 odd

Chapter 5
Section 5.1) 1-12, 13-19 odd, 21, 22, 25, 26
Section 5.2) 1-8, 15-17, 21, 22

MTH 362 - Advanced Engineering Math I

Homework

Chapter 13
Section 13.1)1,2,4,6,8-16
Section 13.2)1-4,9-13odd,15-18,21-27
Section 13.5)2-9,14-17
Section 13.7)5-17odd,22-28

Chapter 7
Section 7.1)8-16
Section 7.2)11-29odd
Section 7.3)1-14
Section 7.8)1-10

Chapter 8
Section 8.1) 1-9,11,12,24
Section 8.2) 10-12
Section 8.3) 1-7

Chapter 1
Section 1.1) 1-6,9-13
Section 1.2) 11
Section 1.3) 1-6,11,12,14,15
Section 1.5) 1-7

Chapter 4
Section 4.1) 11-15
Section 4.3) 1-6,8,10-15

Previous Teaching

Spring 2018, MTH 105 - Elementary Mathematical Codebreaking

Fall 2017, MTH 105 - Elementary Mathematical Codebreaking

Spring 2017, MTH 105, Elementary Mathematical Codebreaking

Spring 2017, MTH 215, Introduction to Linear Algebra

Spring 2017, MTH 362, Advanced Engineering Mathematics I

Fall 2016, MTH 105 - Elementary Mathematical Codebreaking

Fall 2016, MTH 215 - Introduction to Linear Algebra

Fall 2016, MTH 513 - Linear Algebra

Spring 2016, MTH 105 - Elementary Mathematical Codebreaking

Spring 2016, MTH 215 - Introduction to Linear Algebra

Spring 2016, MTH 471/571 - Numerical Analysis

Fall 2015, MTH 105 - Elementary Mathematical Codebreaking

Fall 2015, MTH 215 - Introduction to Linear Algebra

Spring 2015, MTH 105 - Elementary Mathematical Codebreaking

Spring 2015, MTH 418 - Matrix Analysis

Fall 2014, MTH 105 - Elementary Mathematical Codebreaking

Fall 2014, MTH 215 - Introduction to Linear Algebra

Fall 2014, MTH 362 - Advanced Engineering Mathematics

Fall 2014, MTH 513 - Linear Algebra

Spring 2014, MTH 105 - Elementary Mathematical Codebreaking

Spring 2014, MTH 142 - Calculus II

Fall 2013, MTH 105 - Elementary Mathematical Codebreaking

Fall 2013, MTH 142 - Calculus II

Fall 2013, MTH 215 - Introduction to Linear Algebra

Summer 2013, MTH 105 - Elementary Mathematical Codebreaking

Spring 2013, MTH 105 - Elementary Mathematical Codebreaking

Spring 2013, MTH 142 - Calculus II

Fall 2012, MTH 105 - Elementary Mathematical Codebreaking

Fall 2012, MTH 142 - Calculus II

Fall 2012, MTH 513 - Linear Algebra

Summer 2012, MTH 105 - Elementary Mathematical Codebreaking

Spring 2012, MTH 105 - Elementary Mathematical Codebreaking

Spring 2012, MTH 142 - Calculus II

Spring 2012, MTH 362 - Advanced Engineering Mathematics

Fall 2011, MTH 142 - Calculus II

Fall 2011, MTH 471/571 - Numerical Analysis

Spring 2011, MTH 215 - Introduction to Linear Algebra

Spring 2011, MTH 513 - Linear Algebra

Fall 2010, MTH 105 - Elementary Mathematical Codebreaking

Fall 2010, MTH 215 - Introduction to Linear Algebra

Fall 2010, MTH 418 - Matrix Analysis

Spring 2010, MTH 105 - Elementary Mathematical Codebreaking

Spring 2010, MTH 362 - Advanced Engineering Mathematics I

Fall 2009, MTH 132 - Applied Calculus II

Fall 2009, MTH 471/571 - Numerical Analysis

Spring 2009, MTH 215 - Introduction to Linear Algebra

Spring 2009, MTH 362 - Advanced Engineering Mathematics I

Fall 2008, MTH 141 - Introductory Calculus with Analytic Geometry I






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