# Vera Nikolaevna Faddeeva

### Born: 20 September 1906 in Tambov, Russia

Died: 15 April 1983 in Leningrad, USSR (now St Petersburg, Russia)

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**Vera Nikolaevna Faddeeva**'s father was Nikolai Zamyatin (Faddeeva is her married name following her marriage to Dmitrii Konstantinovich Faddeev). She was born in Tambov, a town about 470 km south east of Moscow and 470 km north east of Kharkiv. In 1927 she entered the Faculty of Physics and Mathematics at Leningrad State Pedagogical Institute but transferred in the following year to Leningrad State University. Advised by Nikolai Maksimovich Gyunter (1871-1941), an expert on the Stieltjes integral and its applications to mathematical physics, she graduated in 1930 and, in the same year, married the mathematician Dmitrii Konstantinovich Faddeev. They had three children, one of whom was Ludwig Dmitrievich Faddeev who was educated in the Faculty of Physics at Leningrad State University and went on to become an outstanding mathematician and theoretical physicist producing ideas and results which are at the forefront of today's research.

The years during which Vera Nikolaevna was an undergraduate at Leningrad State University were ones of great difficulty for the academics at the university. During this period independent thinkers were persecuted and N M Gyunter, at that time President of the Leningrad Mathematical Society and a man with a reputation for courage and independent thought, was in great danger. In fact the Leningrad Mathematical Society was disbanded in 1930 following a proposal by the vice-president Vladimir Ivanovich Smirnov, in a successful attempt to save Gyunter's life and the lives of other mathematicians. Following her graduation, Faddeeva worked at the Leningrad Board of Weights and Measures (as her husband had done in the previous couple of years). She was employed as an assistant at the Leningrad Hydraulic Engineering Institute from 1930 to 1934 and, in 1933-34, also as a junior researcher at the Seismology Institute of the USSR Academy of Sciences. For three years, beginning in 1935, she worked as a researcher at the Leningrad Institute of Constructions being part of a team led by Boris Grigorievich Galerkin [3]:-

Faddeeva undertook graduate study at the Leningrad Pedagogical Institute for three years, beginning in 1938. In September 1939, Russia, allied with Germany, invaded Poland from the east. This had little effect on life in Leningrad. However, in June 1941 the course of the war changed dramatically for those living in Russia since Germany invaded their country. By the following month Hitler had plans to take both Leningrad and Moscow. As the German armies rapidly advanced towards Leningrad, many people were evacuated from the city including Faddeeva and her family. For the duration of the siege of Leningrad, Faddeeva lived in Kazan, about 800 km due east of Moscow and considered safe from the German invasion. For a long time there was no opportunity to return to Leningrad which was only liberated from the siege in January 1944. Even after the siege was lifted, access to the devastated city was for a considerable time only possible with a special permit. Faddeeva, together with her husband and other academics, obtained such permits and again Leningrad State University began to operate.During those years, she gained much experience in applied mathematics and sophisticated computational techniques.

She had been appointed as a junior researcher at the Leningrad Division of the Steklov Institute of Mathematics of the USSR Academy of Sciences in 1942 and continued to work for the Institute for the rest of her career. After submitting her candidate's thesis

*On One Problem*in Mathematical Physics to Leningrad State University in 1946 she was awarded the degree (equivalent to a Ph.D.). In 1949 she published the papers

*The method of lines applied to some boundary problems*and

*On fundamental functions of the operator X*

^{{IV}}. In the following year she published two books; one of these was a table of Bessel functions which she wrote in collaboration with Mark Konstantinovich Gavurin (1911-1992), and the other her famous treatise

*Computational methods of linear algebra*. Gavurin was a colleague of Faddeeva and, together with Leonid Vitalyevich Kantorovich, he had set up a computational mathematics unit within the mathematical analysis department at Leningrad State University in 1948. This unit became the basis for the Department of Computational Mathematics set up in 1951. Faddeeva was closely associated with the computational developments by Kantorovich, especially at the Steklov Institute of Mathematics where she became head of the Laboratory of Numerical Computations.

Reviewing Faddeeva's classic 1950 bookAs the head of Laboratory, Vera Nikolaevna guided investigations in various scientific fields related to numerical mathematics. Jointly with S G Mikhlin, she headed the scientific seminar of the Leningrad Division of the Steklov Institute of Mathematics of the USSR Academy of Sciences on numerical methods. The seminar's activity exceeded the limits of the Laboratory. Not only researchers from the Steklov Institute but also many Soviet and foreign scientists working on numerical mathematics took part in the seminar. The Laboratory received many visitors, among whom were such known scientists as James Hardy Wilkinson(Great Britain), George Elmer Forsythe(USA), Richard Steven Varga(USA), Gene Howard Golub(USA), Rózsa Péter(Hungary), Miroslav Fiedler(Czechoslovakia), Axel Ruhe(Sweeden), B D Vulichevich(Yugoslavia), and others.

*Computational methods of linear algebra*, G E Forsythe writes:-

The first chapter of this book was translated into English for the National Bureau of Standards in the United States in 1952 and, in 1959, an English translation of the whole book was published. [12]:-This is a textbook on numerical methods for solving finite systems of linear equations, inverting matrices, and calculating the eigenvalues of finite matrices, all with desk calculators. Although the book is far from exhaustive, the mathematical elegance, the breadth of material, and the number of error-free numerical examples make this by far the finest book to appear in the field.

Olga Taussky-Todd, after giving a similar guide to the contents, writes that the book will serve [13]:-The first chapter of this book forms a clear and well-written introduction to the elementary parts of linear algebra. The second chapter deals with numerical methods for the solution of systems of linear equations and the inversion of matrices, and the third with methods for computing characteristic roots and vectors of a matrix. Most of the important material in these domains is to be found here, and many numerical examples which illustrate the algorithms and point out their merits and deficiencies are given. The discussion is directed principally to the hand computer, and machine computation in the modern sense is hardly present, but the book must be regarded as a valuable guide for the worker in the general area of linear computation.

MathSciNet lists around 40 papers by Faddeeva including 20 joint papers with her husband on numerical analysis including their most famous work, the book... a very useful purpose for researchers, as well as for teachers and students of numerical analysis, because of the clear presentation of the basic facts.

*Computational methods of linear algebra*which appeared in Russian in 1960. This monograph was awarded a State Prize. It was translated into English and published in 1963, the same year in which an enlarged and revised Russian version was published. Note that in 1975 the two authors produced another major work summarizing progress made on numerical linear algebra during the years 1962-1974. Unfortunately the English translation of the 1960 monograph left much to be desired and most reviewers concentrate their comments more on the deficiencies of the translation than on the contents. However, J C P Miller [11] does note that the Russian book is an exceptional work:-

Alston Householder [1] writes:-The original edition of this book in Russian is undoubtedly a very stimulating and valuable book, and translation into English is a very worthwhile task. The content of the book is comprehensive, with much material that does not appear to have been collected together previously.

We mentioned above the 20 joint papers by Faddeeva and her husband, noting that some of the last few of these were:Each edition was, at the time of its appearance, by far the most complete and up-to-date treatment of the subject in print.

*Natural norms in algebraic processes*(1970),

*On the question of the solution of linear algebraic systems*(1974),

*Parallel calculations in linear algebra*(Part 1 in 1977, Part 2 in 1982), and

*A view of the development of numerical methods of linear algebra*(1977). Faddeeva's final paper was the single authored

*Numerical methods of linear algebra in computer formulation*(1984) which is the text of a lecture she gave at the 'Computational mathematics' Conference in Warsaw in 1980.

Finally let us record something of Faddeeva's character [3]:-

Vera Kublanovskaya, who worked with Faddeeva for many years, paints a similar picture [9]:-Faddeeva was not only a remarkable researcher and a notable organizer and manager but also a bright versatile personality. A lively and determined woman, she was sincerely interested in everything that pertained to her institution and cared about her colleagues. Faddeeva loved life and enjoyed it. She was keen on classical music, backpacking trips, and other types of travel. She loved her family and children and took much care of them and her husband. Everyone who knew Faddeeva in person or through her perfect writings will never forget this wonderful researcher and woman.

In the memory of everyone who knew Vera Nikolaevna, she has remained not only a remarkable scientist and excellent organizer but also a brilliant and many-sided personality. She inhered ebullient vitality, firmness of purpose and keen concern about all matters related to the Steklov Institute of Mathematics, her second home, and to her colleagues. Vera Nikolaevna also took trouble about people with whom she was not personally acquainted. She had a talent for enjoying life. Theatre, classical music, travels, and tours were only some of the many passions of this richly endowed person.

**Article by:** *J J O'Connor* and *E F Robertson*

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