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Selected papers of T. N. E. Greville. (English) Zbl 0547.01037

Winnipeg, Canada: The Charles Babbage Research Center, St. Pierre, Manitoba, Canada. XX, 346 p. (1984).
This book contains a complete list of publications of T. N. E. Greville, an autobiographical sketch and a selection of 21 of his papers. These selected papers show that the author has worked successfully in many different areas of mathematics. A comparatively large group of papers deals with problems related to statistical phenomena, from mortality tables to matching problems arising in parapsychological investigations. Other papers are connected with generalized inverses, spline functions and with interpolation. Quite valuable for the reader are the introductions to the six parts of this selection. They are written by Dr. Greville and give insights into motivation, importance and difficulties of the specific problems. The book gives an excellent impression on the scientific activities of a mathematician with high international reputation.
Reviews for these papers appeared in
1. On smoothing a finite table: A matrix approach. J. Soc. industr. appl. Math. 5, 137-154 (1957; Zbl 0080.361).
2. Solutions of the matrix equation \(XAX=X\), and relations between oblique and orthogonal projectors. SIAM J. Appl. Math. 26, 828-832 (1974; Zbl 0288.15018).
3. On a problem concerning band matrices with Toeplitz inverses. Proceedings of the eighth Manitoba Conference on numerical mathematics and computing, Winnipeg 1978, Congr. Numerantium 22, 275-283 (1978, Zbl 0409.15012).
4. With W. F. Trench, Band matrices with Toeplitz inverses. Linear Algebra Appl. 27, 199-209 (1979, Zbl 0428.15002).
5. Bounds for eigenvalues of Hermitian Trench matrices. Numerical mathematics and Computing, Proc. 9th Manitoba Conf., 1979, 241-256 (1980; Zbl 0439.15010).
6. With R. E. Cline, A Drazin inverse for rectangular matrices. Linear Algebra Appl. 29, 53-62 (1980; Zbl 0433.15002).
7. On stability of linear smoothing formulas. SIAM J. Numer. Anal. 3, 157-170 (1966; Zbl 0233.65006).
8. On a problem of E. L. De Forest in iterated smoothing. SIAM J. Math. Anal. 5, 376-398 (1974; Zbl 0252.41023).
9. Moving-weighted-average smoothing extended to the extremities of the data. I. Theory. Scand. Actuarial J. 1981, 39-55 (1981; Zbl 0469.65005).
10. Moving-weighted-average smoothing extended to the extremities of the data. II. Methods. ibid. 1981, 65-81 (1981; Zbl 0498.65006).
11. Moving-weighted-average smoothing extended to the extremities of the data. III. Stability and optimal properties. J. Approximation Theory 33, 43-58 (1981; Zbl 0484.65010).
12. Mortality tables analyzed by cause of death. Record, Amer. Inst. Actuaries 37, 283-294 (1948; Zbl 0037.096).
13. Laws of mortality which satisfy a uniform seniority principle. J. Inst. Actuaries 82, 114-122 (1956; Zbl 0071.139).
14. Spline functions in numerical analysis. Proc. 2nd Manit. Conf. Numer. Math., Winnipeg 1972, 1-17 (1973; Zbl 0312.65007).
15. With I. J. Schoenberg and A. Sharma, The spline interpolation of sequences satisfying a linear recurrence relation. J. Approximation Theory 17, 200-221 (1976; Zbl 0332.41004).
Reviewer: G.Meinardus

MSC:

01A75 Collected or selected works; reprintings or translations of classics
15A09 Theory of matrix inversion and generalized inverses
65D05 Numerical interpolation

Biographic References:

Greville, T. N. E.