What Miller perceived was that in a second-order linear recurrence which has solutions sufficiently differentiated asymptotically, there is a solution that may be uniquely characterized by one initial value and a knowledge of its growth. This led to an algorithm for computing certain solutions of the equation which required only a scant knowledge of their pointwise values.[4]
As the reference says, this technique was subsequently much developed and applied, and was enunciated rather casually by Miller in a 1952 book of tables of Bessel functions.
In the theory of stellation of polyhedra, he made some influential suggestions to H. S. M. Coxeter. These became known as Miller's rules. The 1938 book on the fifty-nine icosahedra resulted, written by Coxeter and Patrick du Val.[6] In the 1930s, Coxeter and Miller found 12 new uniform polyhedra, a step in the process of their complete classification in the 1950s.[7] Miller also made an early investigation into what is now known as the Rule 90cellular automaton.[8]
Dr Miller was married to Germaine Miller (née Gough) in 1934 and had three children (David, Alison and Jane). Germaine died in Cambridge in her 100th year in March 2010 and is buried at St Andrew's Church, Chesterton, Cambridge.
Notesedit
^A brief informal history of the Computer Laboratory
^A. Fletcher, J. C. P. Miller and L. Rosenhead, An index of mathematical tables; this work is mentioned in Diana H. Hook, Jeremy M. Norman, Michael R. Williams, Origins of Cyberspace: A Library on the History of Computing, Networking, and Telecommunications (2002), p. 362, as compiled in 1943, and remaining useful until the 1960s.
^Milton Abramowitz, Irene A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables (1965), p. xiii.
^Wimp, Jet (1984). Computation with recurrence relations. Pitman. p. 162. ISBN978-0273085089.
^Knuth, Donald E. (1981). The Art of Computer Programming, Volume 2: Seminumerical Algorithms (2nd ed.). Addison Wesley. p. 507. ISBN9780201038224.
^Peter R. Cromwell, Polyhedra: "One of the Most Charming Chapters of Geometry" (1999), p. 178.
^Miller, J. C. P. (1970), "Periodic forests of stunted trees", Philosophical Transactions of the Royal Society of London, Series A, Mathematical and Physical Sciences, 266 (1172): 63–111, Bibcode:1970RSPTA.266...63M, doi:10.1098/rsta.1970.0003, JSTOR 73779, S2CID 123330469.
Further readingedit
Doron Zeilberger,The J. C. P. Miller recurrence for exponentiating a polynomial, and its q-analog, Journal of Difference Equations and Applications, Volume 1, Issue 1 1995, pages 57 – 60.
January 01, 1970
miller, jeffrey, charles, percy, miller, august, 1906, april, 1981, english, mathematician, computing, pioneer, worked, number, theory, geometry, particularly, polyhedra, where, miller, monster, refers, great, dirhombicosidodecahedron, early, member, computing. Jeffrey Charles Percy Miller 31 August 1906 24 April 1981 was an English mathematician and computing pioneer He worked in number theory and on geometry particularly polyhedra where Miller s monster refers to the great dirhombicosidodecahedron He was an early member of the Computing Laboratory of the University of Cambridge 1 He contributed in computation to the construction and documentation of mathematical tables 2 and by the proposal of certain algorithms Miller s recurrence algorithm is mentioned in the Handbook of Mathematical Functions 3 What Miller perceived was that in a second order linear recurrence which has solutions sufficiently differentiated asymptotically there is a solution that may be uniquely characterized by one initial value and a knowledge of its growth This led to an algorithm for computing certain solutions of the equation which required only a scant knowledge of their pointwise values 4 As the reference says this technique was subsequently much developed and applied and was enunciated rather casually by Miller in a 1952 book of tables of Bessel functions In volume 2 of The Art of Computer Programming Donald Knuth attributes to Miller a basic technique on formal power series for recursive evaluation of coefficients of powers or more general functions 5 In the theory of stellation of polyhedra he made some influential suggestions to H S M Coxeter These became known as Miller s rules The 1938 book on the fifty nine icosahedra resulted written by Coxeter and Patrick du Val 6 In the 1930s Coxeter and Miller found 12 new uniform polyhedra a step in the process of their complete classification in the 1950s 7 Miller also made an early investigation into what is now known as the Rule 90 cellular automaton 8 Dr Miller was married to Germaine Miller nee Gough in 1934 and had three children David Alison and Jane Germaine died in Cambridge in her 100th year in March 2010 and is buried at St Andrew s Church Chesterton Cambridge Notes edit A brief informal history of the Computer Laboratory A Fletcher J C P Miller and L Rosenhead An index of mathematical tables this work is mentioned in Diana H Hook Jeremy M Norman Michael R Williams Origins of Cyberspace A Library on the History of Computing Networking and Telecommunications 2002 p 362 as compiled in 1943 and remaining useful until the 1960s Milton Abramowitz Irene A Stegun Handbook of Mathematical Functions With Formulas Graphs and Mathematical Tables 1965 p xiii Wimp Jet 1984 Computation with recurrence relations Pitman p 162 ISBN 978 0273085089 Knuth Donald E 1981 The Art of Computer Programming Volume 2 Seminumerical Algorithms 2nd ed Addison Wesley p 507 ISBN 9780201038224 Stellation and facetting a brief history Peter R Cromwell Polyhedra One of the Most Charming Chapters of Geometry 1999 p 178 Miller J C P 1970 Periodic forests of stunted trees Philosophical Transactions of the Royal Society of London Series A Mathematical and Physical Sciences 266 1172 63 111 Bibcode 1970RSPTA 266 63M doi 10 1098 rsta 1970 0003 JSTOR 73779 S2CID 123330469 Further reading editDoron Zeilberger The J C P Miller recurrence for exponentiating a polynomial and its q analog Journal of Difference Equations and Applications Volume 1 Issue 1 1995 pages 57 60 Retrieved from https en wikipedia org w index php title J C P Miller amp oldid 1114106291, wikipedia, wiki, book, books, library,
