It is truly difficult to capture with a single question the essence of research in a diverse and very active area of science and technology, but the query in the title comes very close. This questions was first posed by the late Professor George Forsythe of Stanford University as the underlying rationale for research in computer science, and this study supports his perception. The many different questions, which are posed explicitly and implicitly in these chapters, can be interpreted as special cases of "What Can Be Automated?" The growing realization that the answers to this question are of increasing importance in a crowded world with many interdependent segments is one of the main motivations for this effort.
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THIS DOCUMENT IS AN APPROXIMATE REPRESENTATION OF THE ORIGINAL.
MIT Press, 1980
What Can Be Automated?: The
Computer Science and Engineering
Research Study (COSERS)
Arden, Bruce W.; editor
Table of Contents
1 COSERS Overview ..... 1
About Names and Labels .....5
Some Definitions .....7
A Brief History .....10
Applications .....13
Patterns of Publication .....15
Trends .....18
The Hierarchical World .....28
Prognostication .....29
REFERENCES .....31
2 COSERS Statistics .....33
EDUCATION .....35
NRC/NAS Data .....35
The Production of Ph.D.'s in computer Science .....35
Hamblen Data .....36
National Center for Education Statistics Data .....36
Conclusions About Overall Ph.D. Production .....38
The Taulbee and Conte Data ..... 38
EMPLOYMENT .....39
Ph.D. Specialties .....39
FUNDING .....43
PUBLICATION .....44
REFERENCES .....48
3 Numerical Computation .....51
THE NATURE OF THE AREA .....53
WHY NUMERICAL COMPUTATION IS DIFFICULT .....54
The Science of Numerical Computation .....58
Algorithm Development .....59
Research Successes and Challenges .....61
BACKGROUND CONCEPTS IN NUMERICAL ANALYSIS .....63
Stability and Conditioning .....65
Roundoff Error .....66
Convergence Error and Iteration Methods .....67
Computational Complexity and "Fast" Algorithms .....68
Discretization Error .....68
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What Can Be Automated?: The Computer Science and Engineering Research Study (COSERS)
Jan 01, 1980
MATRIX COMPUTATIONS .....69
Direct Methods .....71
Sparse Elimination and Cyclic Reduction .....72
Iterative Methods .....73
The Eigenvalue Problem .....75
The Generalized Eigenvalue Problem, Ax = λBx .....76
Assessment .....77
OPTIMIZATION AND NONLINEAR EQUATIONS .....80
The nonlinear equation problem .....80
The optimization problem ..... 80
The scope of the field .....81
Significant Problem Parameters .....83
Relationship to Other Areas of Mathematical Science .....85
A Short History An Assessment .....86
ORDINARY DIFFERENTIAL EQUATIONS .....90
The Ordinary Differential Equation Problem .....92
Significant Problem Parameters .....93
Relationship to Other Areas of Mathematical Science .....94
PARTIAL DIFFERENTIAL EQUATIONS .....96
Prototypes of Partial Differential Equations .....97
Numerical Methods .....98
Chronological Development .....103
Relationship to Other Areas of Science .....105
An Assessment .....106
MATHEMATICAL SOFTWARE .....108
Chronological Development and Assessment .....110
CURVES, SURFACES, AND GRAPHICS .....111
The Nature of the Problem .....111
Chronological Development .....112
Current Research and Future Projections .....114
RESEARCH HIGHLIGHTS OF OTHER AREAS .....117
Evaluating Mathematical Functions .....117
Numerical Integration .....118
The Monte Carlo Method .....119
Parallel Computation .....120
Integral Equations .....121
Arithmetic and Architecture .....122
Computational Complexity and Fast Methods .....124
Computing Polynomial Zeros .....124
THE RESEARCH ENVIRONMENT IN NUMERICAL COMPUTATION .....125...
