Project 19: Analytic algorithms and symbolic manipulation
Amsterdam 1977:
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The Modular Analysis of Algorithms and Programs: N.N. Yanenko
The paper by Professor Yanenko discussed the technological chain of
modern computational mathematics.
He noted that the structure of the ensuing program is conditioned by
many factors. Essential factors are the structure of the algorithm; the
structure of the computer; the need for the free exchange of programs; the
need for co-operation, distribution of programming jobs and testing in
program preparation (where each aspect can be aided by the use of
structured programming); the need for flexibility and evolution as
built-in features of program design; and the need for an effective program.
Professor Yanenko observed that the last (but not least) item is a most
important condition for the successful development of numerical
(computational) mathematics. The modular structuring of algorithms and
hence of programs was the basis of all effective modern programming.
Several definitions of modular structure were available in the literature.
He preferred that given by Dennis.
Professor Yanenko took a classic problem of mathematical physics by way
of example and gave an excellent detailed analysis of problem solution
through use of the technological chain given above.
Novosibrisk 1979:
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Talks were given by N N Yanenko, W S Brown, V M Matrosov, and V L Rvatchov.
Brown referred to Comp. Phys. Comm. 17 (1979) 207-215.
Madison 1982:
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There was some discussion as to whether the group should regard
symbolic manipulation as within its scope. If not, then by TC2
requirements it should suggest that another group be formed. Einarsson
remarked on its importance as an aid to numerical work and pointed out
that two talks at Boulder on the topic strongly suggested that the
group regarded it as within its scope. It was agreed that the present
vague topic should be dropped but that the group hopes to establish
more precise projects later.
Como 1987:
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In the absence of Shokin, Stetter remarked that the intention of the
project continued to be important and he would not like to have it
lost. With the aid of symbolic computation facilities a good number of
old and new mathematical techniques could be utilized for scientific
computation if they were combined with numerical analysis proper. At
the same time, members of the symbolic computation community realize
that a stronger impact of their work on scientific computation will
depend on the development of software which also includes numerical
procedures.
Stetter will attend the EUROCAL meeting in Leipzig at the beginning of
June. He will inform the group about aspects which may be interesting
for the group. Eventually, PSE should encompass symbolic and numerical
computation in a unified way.
A discussion followed. It was concluded that cooperation with the
symbolic computation community is needed, and that the WG 2.5 should
help as much as possible where numerical work is concerned.
(Gentleman, Ford, Delves, Gaffney, Reid)
Stetter proposed that the project remain active, and he offered to
coordinate it. This was accepted by IFIP/WG 2.5.
Stanford 1988:
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Documents:
IFIP/WG 2.5 (Stanford-17) 1517, 1 page.
IFIP/WG 2.5 (Stanford-32) 1532, 27 pages, (only for WG 2.5 internal use).
H. Stetter submitted the report entitled "Analytic Algorithms and
Symbolic Manipulation" (1517) by mail.
The following is the summary of the report presented by M. Gentleman
There are significant funding incentives by several U.S. agencies,
especially NSF for symbolic algebra systems for teaching calculus,
problem solving for scientists and engineers, etc. The interface
between numerical and symbolic computation is emphasized.
Commercially available systems, based on common microcomputers and
workstations, have taken an aggressive step forward, and have shifted
from being merely languages where the basic values are algebraic
expressions to being problem solving environments complete with
numerical calculation, graphical display of results, and automatic
choice of algorithms.
A paper written by Yu. Shokin and Z. Fedotova entitled "Review of
Papers of Soviet Authors on Symbolic Manipulation" (submitted by B.
Einarsson) is available as document number 1532.
Beijing 1989:
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H. Stetter summarized the work relating to project 19. He said that
there had been no joint activity of the project group, but project
members have been individually active.
Observations:
(i) Two most recent "computer math" systems (Mathematica, Wolfram Res;
Derive, successor to mu-math, Soft Warehouse) have excellent user
interfaces and graphics, but they are stand- alone PSE's without
interfaces to other software. Symbolic facilities are not available in
numerical packets.
(ii) Interaction within "computer algebra" community has considerably
improved. However, there is still very little (if any) serious
interaction with computational mathematics.
Conclusions:
Main goal of the project is to further the use of analytic (symbolic)
methods to enhance computational work (in floating point). This work
is still in infancy, so WG 2.5 should continue working in this area.
Suggested actions:
Formulation of the needs (from computational point of view).
Involvement from Computer Algebra and Numerics communities.
In the discussion it was noted that one of the more specific aims for symbolic manipulation
should be the handling of singularities, and ODE's. Kulisch said that a language for ODE's may
be one solution to the problem. Rice noted that NSF recently held a workshop on symbolic
computation in support of computer algebra, and that the report from that workshop is very
relevant to numerical computations. Fosdick and Rice were of the opinion that we should urge
the symbolic algebra package writers to put hooks into the packages so that they can be used in
numerical computation applications. Currently it is not easy to use these packages except as
stand-alone environments.
Jerusalem 1990:
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H. Stetter summarized the work relating to project 19. He pointed out
that currently there is no standardized way of handling functions as
data, and that a discussion of this problematics may make an
interesting ICIAM minisymposium. Discussion developed (Feldman,
Gaffney, Stetter, Rice, Kulisch)
Karlsruhe 1991:
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H. Stetter summarized the work relating to project 19. A minisymposium
related to the project was held at ICIAM 91 (see below)
ICIAM, 1991.
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Document: IFIP/WG 2.5 (Karlsruhe-17) 1817, 3 pages,
The Second International Conference on Industrial and Applied
Mathematics was held in Washington, D.C., between 8 and 12 July 1991.
Three minisymposia were organized by the IFIP WG 2.5 members during
ICIAM 1991:
- J. Reid, "Fortran 90: How the New Language will Benefit Applied
Mathematics."
- S. Feldman and M. Vouk, "Scientific and Numerical Computing in C."
- H. J. Stetter, "Use of Automatically Derivable Analytic Information
in Numerical Computation."
All three minisymposia were well attended and well received. Summary
of the content of the minisymposia is given in document 1817.
Toronto 1992:
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H. Stetter summarized the work relating to project 19.