Curriculum vitae

 

Studies

  

1966 Newark Senior High School, Newark, Delaware, U.S.A. (A.F.S. scholarship)
1970 University of Athens, Greece, Department of Mathematics
1971 Degree in Education from SELETE, a UN school in Athens, Greece
1972 Masters Degree in Operational Research from the University of Southampton, United Kingdom
1972-73 Institute of Applied Mathematics of the University of Heidelberg, Germany
1974-75 Computer Science Department of the University of Kaiserslautern, Germany
1976

Masters degree in Computer Science from the University of Wisconsin-Madison, U.S.A.

1978

Ph.D. in Computer Science-Operations Research from North Carolina State University in Raleigh, U.S.A.

  

Professional Experiences

 

1.

Teaching Assistant at the Universities of Heidelberg and NCSU

2.

Research Assistant at the Universities of Wisconsin and Kaiserslautern

3.

Assistant Professor at the University of Athens, Unit of Applied Mathematics; Fall     semester of 1979

4.

Visiting Assistant Professor at the University of Kansas, Department of Computer Science; Spring semester 1980

5.

Assistant Professor at the University of Kansas, Department of Computer Science; Fall semester 1980 to summer 1984

6.

Intra-University Professor at the University of Kansas, Department of Electrical Engineering; 1983-84

7.

Associate Professor at the University of Kansas, Department of Computer Science; Fall semester 1984 to summer 1996

8.

Visiting Professor at the National Technical University of Athens, Greece, Department of Electrical and Computer Engineering; Spring semester of 1987. (United Nations Development Program - TOKTEN - consultant.)

9.

Visiting Professor at Moscow State University (Lomonossov), U.S.S.R., Department of Mechanics and Mathematics; Spring semester of 1990.  (Fulbright Scholar.)

10.

Member of the Russian and East European Studies (REES) Program of the University of Kansas;  Spring semester 1993.

11.

Professor at the University of Kansas, Department of Computer Science; Fall semester 1996.

12.

Associate Professor at the University of Thessaly, Department Theoretical and Applied Sciences (1998-2000) and Department of Computer and Communication Engineering; Fall semester 2001 to 2004.

13.

Professor at the University of Thessaly, Department of Electrical and Computer Engineering; Fall semester 2004 to present.

 

Erasmus

 

He has been /Erasmus/Socrates coordinator/ of the Department of Computer and Communications Engineering since 2002 and the /Erasmus LLP delegate/ since 2008.
He has signed partnership agreements with the following universities: Vilnius 01 (LT), München 02 (TUM, DE), Madrid 05 (E), Sevilla 01 (E), Sakarya 01 (TR), Istanbul 14 (TR), Bucurest 09 (RO), Praha 10 (CZ), Sofia 06 (BG), Sofia 16 (BG), Perugia 01 (I), Turku 01 (SF), Turku 02 (SF).

 

Prizes and Awards

 

1.

First Prize: The paper "A new method for polynomial real root isolation" (Publication No. 3) received the First Prize in the student paper competition of the ACM conference in Atlanta, Georgia, 1978.

2.

Intra-University Professorship: Academic year 1983-84one of six Intra-University Professorships awarded that year; to be associated with the Department of Electrical Engineering of the University of Kansas.

3.

Sabbatical leave: Spring semester of 1987; to complete the writing of a book  and teach at the Electrical and Computer Engineering Department of the National Technical University of Athens.  (United Nations Development Program - TOKTEN - consultant.)

4.

Fulbright grant: Summer (June and July) of 1989; to intensively study Russian at the Bryn Mawr College Russian Language Institute.

5.

Fulbright grant: Spring Semester of 1990; to teach Computer Algebra at the Department of Mechanics and Mathematics of the Moscow State University (Lomonossov), U.S.S.R.

6.

NSF grant: Spring Semester of 1992; to create a mathematical computing laboratory (Co-Principal Investigator).

7.

Sabbatical leave: Academic year 1995-96; to complete the writing of another book.

 

New Methods Developed

 

The following forgotten papers were rediscovered by Akritas: Vincent's paper of 1836 (in 1975, see publications 5, 16), and Lloyd's paper "On the forgotten Mr. Vincent" Sylvester's paper of 1853 and Van Vleck's paper of 1899 (in 1985), and Sylvester's determinant identity of 1851 (in 1992).  Based on these papers the following methods were developed:

   
1.

The Vincent-Collins-Akritas bisection method for isolating the real roots of a polynomial equation see publication 1; misleadingly, some authors refer to it as the "Descartes' method". The method was developed immediately after Akritas' discovery of Vincent's paper, and has been implemented in the computer algebra system maple; an excellent presentation of the method, along with a complete example, can be found in the (French) lecture notes of the University of Lille, France. As Alesina and Galuzzi (1998a) point out, the Vincent-Collins-Akritas method is one way of implementing Vincent's theorem; see also their second paper (1998b). Moreover, Alesina and Galuzzi masterly used Vincent's theorem and Obreschkoff's work of 1920-23, (which was also independently rediscovered by Ostrowski in 1950) to prove that the Vincent-Collins-Akritas method terminates. See the papers by Mehlhorn et al. (2006), Yap et al (2006) and Sharma's PhD Thesis; in all these the Vincent-Collins-Akritas method is being misleadingly referred to as "Decartes' method".

2.

The Vincent-Akritas-Strzebonski continued fractions method for isolating the real roots of a polynomial equation (see publications 3, 11, 14, 19, 22, 28, 41, 58).  The method was developed in 1978 and it has been implemented in: (a) the computer algebra system Mathematica and (b) the open source algebraic library SYNAPS (see the paper by Tsigaridas and Emiris). It has been demonstrated both theoretically and empirically, that it is the fastest real root isolation method existing; see the papers 58 and Tsigaridas and Emiris. As Alesina and Galuzzi (1998a) point out, the Vincent-Akritas-Strzebonski method is another way of implementing Vincent's theorem. Moreover, Alesina and Galuzzi masterly used Vincent's theorem and Obreschkoff's work of 1920-23, (which was also independently rediscovered by Ostrowski in 1950) to prove that the Vincent-Akritas-Strzebonski method terminates. Of interest are Vikram Sharma's PhD Thesis and paper (2007), where this method if referred to as Akritas' continued fractions method. Sharma removed the hypothesis of the "ideal" positive lower root bound and showed that the Vincent-Akritas-Strzebonski method is still polynomial in time.

3.

A method for approximating the real roots of a polynomial equation (see publications 23, 24). This method uses continued fractions, an idea by Lagrange and Vincent's theorem.  It was developed in 1981 together with K.H. Ng.

4.

A subresultant method for computing polynomial remainder sequences (prs's) (see publications 29, 31, 32, 33, 34, 35, 36).  Developed in 1986, this is the "best" method for computing prs's, in the sense that the coefficients obtained are the smallest possible (without gcd computations).  It is based on the papers by Sylvester and Van Vleck and it is unique in that it does not perform actual polynomial divisions but matrix triangularization.

5.

A new, improved, matrix triangularization subresultant method for computing polynomial remainder sequences (see publications 40, 43).  It is based on Sylvester's determinant identity and it is an improvement over the above method (4)  in the sense that the theoretical results obtained are independent of Van Vleck's theorem (which cannot always be used); moreover, now a matrix of smaller order is being transformed and the sign of the coefficients is computed exactly.  Developed in 1992 together with E. K. Akritas and G. I. Malashonok.

6.

An improved (faster) variant of the matrix-triangularization subresultant prs method for the computation of a greatest common divisor of two polynomials along with their polynomial remainder sequence (see publication 51).  The improvement is based on the work of Malaschonok who proposed a new, recursive method for the solution of systems of linear equations in integral domains. The complexity is the same as the complexity of matrix multiplication. Developed in 2000 together with G. I. Malashonok.

7.

A new (linear complexity) method for computing upper bounds on the positive roots of polynomials; see publication 69. This method is based on a generalization and an extension of a theorem by Doru Stefanescu and gives the sharpest upper bounds on the positive roots (among all existing methods such as Cauchy, Lagrange, Kioustelidis etc). Using our new method to compute positive root bounds we were able to improve the performance of the Vincent-Akritas-Strzebonski continued fractions real root isolation method; especially for the case of very many very large roots the improvement was in the order of 300%.

8.

A new (quadratic complexity) method for computing upper bounds on the positive roots of polynomials; see publications 75 and 76. Using our new quadratic complexity bound we were able to further improve the performance of the Vincent-Akritas-Strzebonski continued fractions real root isolation method, making it the fastest for all classes of polynomials.

9.

A new method for computing subresultant polynomial remainder sequences; see publication 92. It is based on Sylvester's form of the resultant of 1853 and uses a Theorem by Pell and Gordon of 1917.

10.

Extended Van Vleck's matrix triangularization method to compute both complete and incomplete Sturm sequences; see publication 93. Used a totally forgotten theorem of 1917 by Pell and Gordon.

11.

Three new methods for computing subresultant polynomial remainder sequences; see publication 94.

Back to home page