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GIANFRANCO CIMMINO’S CONTRIBUTIONS TO NUMERICAL MATHEMATICS
, 2004
"... Gianfranco Cimmino (19081989) authored several papers in the field of numerical analysis, and particularly in the area of matrix computations. His most important contribution in this field is the iterative method for solving linear algebraic systems that bears his name, published in 1938. This pape ..."
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Gianfranco Cimmino (19081989) authored several papers in the field of numerical analysis, and particularly in the area of matrix computations. His most important contribution in this field is the iterative method for solving linear algebraic systems that bears his name, published in 1938. This paper reviews Cimmino’s main contributions to numerical mathematics, together with subsequent developments inspired by his work. Some background information on Italian mathematics and on Mauro Picone’s Istituto Nazionale per le Applicazioni del Calcolo, where Cimmino’s early numerical work took place, is provided. The lasting importance of Cimmino’s work in various application areas is demonstrated by an analysis of citation patterns in the broad technical and scientific literature.
How ordinary elimination became Gaussian elimination
 Historia Math
"... Newton, in an unauthorized textbook, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Newton did not want to publish, that Euler did not recommend, that Legendre called “ordinary, ” and that Gauss called “common ” ..."
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Cited by 8 (1 self)
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Newton, in an unauthorized textbook, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Newton did not want to publish, that Euler did not recommend, that Legendre called “ordinary, ” and that Gauss called “common ” — is now named after Gauss: “Gaussian ” elimination. (One suspects, he would not be amused.) Gauss’s name became associated with elimination through the adoption, by professional computers, of a specialized notation that Gauss devised for his own least squares calculations. The notation allowed elimination to be viewed as a sequence of arithmetic operations that were repeatedly optimized for hand computing and eventually were described by matrices. In einem unautorisierten Textbuch beschreibt Newton den Prozess für die Lösung von simultanen Gleichungen, den spätere Autoren speziell für lineare Gleichungen anwandten. Diese Methode — welche Newton
MAURO PICONE, SANDRO FAEDO, AND THE NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATIONS IN ITALY (1928–1953)
"... Abstract. In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885–1977) and Sandro Faedo (1913–2001). We argue that while the development of constructive methods for the solution of PDEs was cen ..."
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Abstract. In this paper we revisit the pioneering work on the numerical analysis of partial differential equations (PDEs) by two Italian mathematicians, Mauro Picone (1885–1977) and Sandro Faedo (1913–2001). We argue that while the development of constructive methods for the solution of PDEs was central to Picone’s vision of applied mathematics, his own work in this area had relatively little direct influence on the emerging field of modern numerical analysis. We contrast this with Picone’s influence through his students and collaborators, in particular on the work of Faedo which, while not the result of immediate applied concerns, turned out to be of lasting importance for the numerical analysis of timedependent PDEs.