Marina Arav

Marina Arav

Associate Professor

Office: 776 COE
Office phone: 404.413.6443
E-mail: matmxa [at]langate.gsu.edu
Personal webpage

Education

B.S. Applied Mathematics Simferopol State University, Ukraine, 1990
M.S. Applied Mathematics Technion, Israel, 1995
Ph.D. Applied Mathematics Technion, Israel, 2000

Research/Teaching

Courses I taught:

College Algebra, Precalculus, Advanced Mathematics, all levels of Calculus, Differential Equations, Introductory Linear Algebra, Linear Algebra, Advanced Matrix Analysis, Undergraduate Research course in Sign Pattern Matrices, Undergraduate Research course in Matrix Factorizations Methods, Undergraduate Research course on Applications of SVD in Image Processing, Graduate Research course on Nonnegative Matrix Factorization Algorithms, Thesis Research course on Applications of SVD and PCA in Image Reconstruction, Thesis Research course on Neuron Image Reconstruction using Matrix Algorithms, Thesis Research course on Functions of Matrices: Square Root Function of Matrices, Thesis Research course on Functions of Matrices: Exponential Function of Matrices, Thesis Research course on Nonnegative Matrix Factorization Algorithms.

I am a Mentor in the undergraduate program RIMMES, and an Advisor on the Board of The Mathematics and Statistics Club of GSU.

My Research Interests include: Matrix Analysis, Linear Algebra, Numerical Linear Algebra, Math Education, Mathematical Programming, Bioinformatics, Fixed Point Theory, Statistical Analysis, Data Analysis.

Selected Publications

M. Arav, D. Hershkowitz, V. Mehrmann, H. Schneider, The Recursive Inverse Eigenvalue Problem, SIAM Journal on Matrix Analysis and Applications (SIMAX), 22, 392-412, 2000.

M. Arav, Application Techniques of the Recursive Inverse Eigenvalue Problem Solution Algorithm, Ideas, Projects and Technologies, ECI-S, 3, 2-8, 2004.

T. I. Seidman, H. Schneider, M. Arav, Comparison Theorems Using General Cones for Norms of Iteration Matrices, Linear Algebra and Its Applications, 399, 169-186, 2005.

M. Arav, F. Hall, S. Koyuncu, Z. Li, and B. Rao, Rational Realizations of the Minimum Rank of a Sign Pattern Matrix, Linear Algebra and Its Applications, 409, 111-125, 2005.

K. Hayashi, M. Arav, Bayesian Factor Analysis when Only a Sample Covariance Matrix is Available, Educational and Psychological Measurement, 66, 272-284, 2006.

M. Arav, S. Reich, A. J. Zaslavski, A Note on the Minimization of Convex Functions, International Journal of Pure and Applied Mathematics, 32, 65-70, 2006.

M. Arav, F. E. Castillo Santos, S. Reich and A. J. Zaslavski, A Note on Asymptotic Contractions, Fixed Point Theory and Applications, Volume 2007, Article ID 39465, 1-6, 2007.

M. Arav, S. Reich and A. J. Zaslavski, Uniform Convergence of Iterates for a Class of Asymptotic Contractions, Fixed Point Theory, Volume 8, No. 1, 3-9, 2007.

M. Arav, J. Bevis, F. J. Hall, Inherited LU-Factorizations of Matrices, to appear in Linear Algebra and Its Applications.

M. Arav, Contour Approximation of Data and the Harmonic Mean, to appear in Mathematical Inequalities and Applications, Volume 11, 2008.

M. Arav, F. J. Hall, Z. Li , A Cauchy-Schwarz Inequality for Triples of Vectors, to appear in Mathematical Inequalities and Applications, Volume 11, 2008.