Richard S. Varga
Encyclopedia
Richard Steven Varga is an American
mathematician who specializes in numerical analysis
and linear algebra
. He is currently a University Professor of Mathematical Sciences at Kent State University
, Kent, Ohio
. Varga is known for his contributions to many areas of mathematics, including matrix analysis
, complex analysis
, approximation theory
, and scientific computation
. He is the author of the classic textbook Matrix Iterative Analysis. Varga has been the Editor-in-Chief the journal Electronic Transactions on Numerical Analysis (ETNA).
of Hungarian-born parents in 1928. He obtained a bachelor's degree in mathematics from Case Institute of Technology (present Case Western Reserve University
) in 1950. Varga was a member of the collegiate wrestling
team of Case.
Following the advice of Professor Max Morris at Case, Varga joined Harvard University
for the master's degree and obtained an A.M. in mathematics. Continuing his doctoral work at Harvard under the supervision of Joseph L. Walsh
, Varga worked on the theory of rational approximation of complex
analytic function
s. Varga received his Ph.D. degree in 1954 with a dissertation Properties of a Special Set of Entire Functions
and their Respective Partial Sums.
While at Harvard, Varga also studied with Garrett Birkhoff
, who later came to collaborate with Varga in research both on iterative method
s for differential equations and on positive matrices (and positive operators on partially ordered vector space
s).
in Pittsburgh. In 1960 he returned to Case Institute of Technology as a Professor of mathematics and remained there for the next nine years. He then moved to Kent State University as University Professor of mathematics. At Kent Varga has held numerous academic positions, including Director (1980–1988) and Research Director (1988–2006) of the Institute for Computational Mathematics. His work includes numerical analysis---particularly iterative methods in numerical linear algebra, matrix theory, and differential equations---complex approximation theory---particularly Pad'e approximation (often with Edward B. Saff, Jr.)---and analytic number theory, including high-precision calculations related to the Riemann hypothesis
. He is also known for advocating experimentation in mathematics, and for writing a monograph surveying his contributions on scientific computing to resolve open problems and conjectures.
United States
The United States of America is a federal constitutional republic comprising fifty states and a federal district...
mathematician who specializes in numerical analysis
Numerical analysis
Numerical analysis is the study of algorithms that use numerical approximation for the problems of mathematical analysis ....
and linear algebra
Linear algebra
Linear algebra is a branch of mathematics that studies vector spaces, also called linear spaces, along with linear functions that input one vector and output another. Such functions are called linear maps and can be represented by matrices if a basis is given. Thus matrix theory is often...
. He is currently a University Professor of Mathematical Sciences at Kent State University
Kent State University
Kent State University is a public research university located in Kent, Ohio, United States. The university has eight campuses around the northeast Ohio region with the main campus in Kent being the largest...
, Kent, Ohio
Kent, Ohio
Kent is a city in the U.S. state of Ohio and the largest city in Portage County. It is located along the Cuyahoga River in Northeastern Ohio on the western edge of the county. The population was 27,906 at the 2000 United States Census and 28,904 in the 2010 Census...
. Varga is known for his contributions to many areas of mathematics, including matrix analysis
Matrix (mathematics)
In mathematics, a matrix is a rectangular array of numbers, symbols, or expressions. The individual items in a matrix are called its elements or entries. An example of a matrix with six elements isMatrices of the same size can be added or subtracted element by element...
, complex analysis
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
, approximation theory
Approximation theory
In mathematics, approximation theory is concerned with how functions can best be approximated with simpler functions, and with quantitatively characterizing the errors introduced thereby...
, and scientific computation
Computational science
Computational science is the field of study concerned with constructing mathematical models and quantitative analysis techniques and using computers to analyze and solve scientific problems...
. He is the author of the classic textbook Matrix Iterative Analysis. Varga has been the Editor-in-Chief the journal Electronic Transactions on Numerical Analysis (ETNA).
Birth and education
Richard Varga was born in Cleveland, OhioOhio
Ohio is a Midwestern state in the United States. The 34th largest state by area in the U.S.,it is the 7th‑most populous with over 11.5 million residents, containing several major American cities and seven metropolitan areas with populations of 500,000 or more.The state's capital is Columbus...
of Hungarian-born parents in 1928. He obtained a bachelor's degree in mathematics from Case Institute of Technology (present Case Western Reserve University
Case Western Reserve University
Case Western Reserve University is a private research university located in Cleveland, Ohio, USA...
) in 1950. Varga was a member of the collegiate wrestling
Collegiate wrestling
Collegiate wrestling, sometimes known in the United States as Folkstyle wrestling, is a style of amateur wrestling practised at the collegiate and university level in the United States. Collegiate wrestling emerged from the folk wrestling styles practised in the early history of the United States...
team of Case.
Following the advice of Professor Max Morris at Case, Varga joined Harvard University
Harvard University
Harvard University is a private Ivy League university located in Cambridge, Massachusetts, United States, established in 1636 by the Massachusetts legislature. Harvard is the oldest institution of higher learning in the United States and the first corporation chartered in the country...
for the master's degree and obtained an A.M. in mathematics. Continuing his doctoral work at Harvard under the supervision of Joseph L. Walsh
Joseph Leonard Walsh
Joseph Leonard Walsh, was an American mathematician. His work was mainly in the field of analysis.For most of his professional career he studied and worked at Harvard University. He received a B.S. in 1916 and a PhD in 1920. The Advisor of his PhD was Maxime Bôcher...
, Varga worked on the theory of rational approximation of complex
Complex analysis
Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is useful in many branches of mathematics, including number theory and applied mathematics; as well as in physics,...
analytic function
Analytic function
In mathematics, an analytic function is a function that is locally given by a convergent power series. There exist both real analytic functions and complex analytic functions, categories that are similar in some ways, but different in others...
s. Varga received his Ph.D. degree in 1954 with a dissertation Properties of a Special Set of Entire Functions
Entire function
In complex analysis, an entire function, also called an integral function, is a complex-valued function that is holomorphic over the whole complex plane...
and their Respective Partial Sums.
While at Harvard, Varga also studied with Garrett Birkhoff
Garrett Birkhoff
Garrett Birkhoff was an American mathematician. He is best known for his work in lattice theory.The mathematician George Birkhoff was his father....
, who later came to collaborate with Varga in research both on iterative method
Iterative method
In computational mathematics, an iterative method is a mathematical procedure that generates a sequence of improving approximate solutions for a class of problems. A specific implementation of an iterative method, including the termination criteria, is an algorithm of the iterative method...
s for differential equations and on positive matrices (and positive operators on partially ordered vector space
Ordered vector space
In mathematics an ordered vector space or partially ordered vector space is a vector space equipped with a partial order which is compatible with the vector space operations.- Definition:...
s).
Career
From 1954 until 1960, Varga worked for Bettis Atomic Power LaboratoryBettis Atomic Power Laboratory
Bettis Atomic Power Laboratory is a U.S. Government-owned, contractor-operated research and development facility located in the Pittsburgh suburb of West Mifflin, Pennsylvania. It solely focuses on the design and development of nuclear power for the U.S. Navy....
in Pittsburgh. In 1960 he returned to Case Institute of Technology as a Professor of mathematics and remained there for the next nine years. He then moved to Kent State University as University Professor of mathematics. At Kent Varga has held numerous academic positions, including Director (1980–1988) and Research Director (1988–2006) of the Institute for Computational Mathematics. His work includes numerical analysis---particularly iterative methods in numerical linear algebra, matrix theory, and differential equations---complex approximation theory---particularly Pad'e approximation (often with Edward B. Saff, Jr.)---and analytic number theory, including high-precision calculations related to the Riemann hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
. He is also known for advocating experimentation in mathematics, and for writing a monograph surveying his contributions on scientific computing to resolve open problems and conjectures.