dorsal/arxiv
View SchemaA Continuous Model of Computation
| Authors | J. F. Traub |
|---|---|
| Categories | |
| ArXiv ID | physics/0106045 |
| URL | https://arxiv.org/abs/physics/0106045 |
| Journal | Physics Today, May, 1999, 39-43 |
Abstract
Although the Turing-machine model of computation is widely used in computer science it is fundamentally inadequate as a foundation for the theory of modern scientific computation. The real-number model is described as an alternative. Physicists often choose continuous mathematical models for problems ranging from the dynamical systems of classical physics to the operator equations and path integrals of quantum mechanics.These mathematical models use the real or complex number fields and we argue that the real-number model of computation should be used in the study of the computational complexity of continuous mathematical models. The study of continuous complexity is called information-based complexity. In this expository article we apply information-based complexity to topics such as breaking the curse of dimensionality, approximating the calculation of path integrals, and solving ill-posed problems. Precise formulations of these ideas may be found in J. F. Traub and A. G. Werschulz, "Complexity and Information", Cambridge University Press, 1998.
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"abstract": "Although the Turing-machine model of computation is widely used in computer\nscience it is fundamentally inadequate as a foundation for the theory of modern\nscientific computation. The real-number model is described as an alternative.\nPhysicists often choose continuous mathematical models for problems ranging\nfrom the dynamical systems of classical physics to the operator equations and\npath integrals of quantum mechanics.These mathematical models use the real or\ncomplex number fields and we argue that the real-number model of computation\nshould be used in the study of the computational complexity of continuous\nmathematical models.\n The study of continuous complexity is called information-based complexity. In\nthis expository article we apply information-based complexity to topics such as\nbreaking the curse of dimensionality, approximating the calculation of path\nintegrals, and solving ill-posed problems. Precise formulations of these ideas\nmay be found in J. F. Traub and A. G. Werschulz, \"Complexity and Information\",\nCambridge University Press, 1998.",
"arxiv_id": "physics/0106045",
"authors": [
"J. F. Traub"
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"journal_ref": "Physics Today, May, 1999, 39-43",
"title": "A Continuous Model of Computation",
"url": "https://arxiv.org/abs/physics/0106045"
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