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HYBRID SYMBOLIC-NUMERIC COMPUTATION

Lihong Zhi

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Abstract

Symbolic computation and numeric computation are two types of computation for solving problems arising from science and engineering.Symbolic computation produces exact global solutions but is usually very expensive due to large symbolic expression;In contrast, numeric computation is fast but only produces approximate local solutions.Especially,for ill- conditioned problems,numeric algorithms converge very slowly and may return wrong results sometimes.In this paper,we emphasize the relationship between symbolic computation and numeric computation and explain how to integrate these two computations effectively to solve problems which can not be solved by using one type of computation.We also introduce some new results in the emerging area of hybrid symbolic-numeric computation.

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What this paper is about

Symbolic computation and numeric computation are two types of computation for solving problems arising from science and engineering.Symbolic computation produces exact global solutions but is usually very expensive due to large symbolic expression;In contrast, numeric computation is fast but only produces approximate local solutions.Especially,for ill- conditioned problems,numeric algorithms converge very slowly and may return wrong results sometimes.In this paper,we emphasize the relationship between symbolic computation and numeric computation and explain how to integrate these two computations effectively to solve problems which can not be solved by using one type of computation.We also introduce some new results in the emerging area of hybrid symbolic-numeric computation.

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Available abstract

Symbolic computation and numeric computation are two types of computation for solving problems arising from science and engineering.Symbolic computation produces exact global solutions but is usually very expensive due to large symbolic expression;In contrast, numeric computation is fast but only produces approximate local solutions.Especially,for ill- conditioned problems,numeric algorithms converge very slowly and may return wrong results sometimes.In this paper,we emphasize the relationship between symbolic computation and numeric computation and explain how to integrate these two computations effectively to solve problems which can not be solved by using one type of computation.We also introduce some new results in the emerging area of hybrid symbolic-numeric computation.

Key concepts: Symbolic-numeric computation, Computation, Symbolic computation, Computer science, The Symbolic, Symbolic data analysis, Theoretical computer science, Algorithm

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