Bit Complexity of Computing Solutions for Symmetric Hyperbolic Systems of PDEs (Extended Abstract)

We establish upper bounds of bit complexity of computing solution operators for symmetric hyperbolic systems of PDEs. Here we continue the research started in our papers of 2009 and 2017, where computability, in the rigorous sense of computable analysis, has been established for solution operators of Cauchy and dissipative boundary-value problems for such systems.

[1]  R. Loos.  Computing in Algebraic Extensions , 1983 .

[2]  Victor L. Selivanov,et al.  Computing Solution Operators of Boundary-value Problems for Some Linear Hyperbolic Systems of PDEs , 2013, Log. Methods Comput. Sci..

[3]  V. L. Selivanov,et al.  On Constructive number fields and computability of solutions of PDEs , 2017 .

[4]  K. Friedrichs.  Symmetric hyperbolic linear differential equations , 1954 .

[5]  Alkiviadis G. Akritas,et al.  Elements of Computer Algebra with Applications , 1989 .

[6]  Victor Y. Pan,et al.  The bit-complexity of discrete solutions of partial differential equations: Compact multigrid , 1990 .

[7]  Martin Ziegler,et al.  A Computable Spectral Theorem , 2000, CCA.

[8]  László Lovász,et al.  Factoring polynomials with rational coefficients , 1982 .

[9]  A. Kulikovskii,et al.  Mathematical Aspects of Numerical Solution of Hyperbolic Systems , 1998, physics/9807053.

[10]  David W. Lewis,et al.  Matrix theory , 1991 .

[11]  Alexander Schrijver,et al.  Theory of linear and integer programming , 1986, Wiley-Interscience series in discrete mathematics and optimization.

[12]  Klaus Weihrauch,et al.  A Tutorial on Computable Analysis , 2008 .

[13]  Victor L. Selivanov,et al.  Polynomial-Time Presentations of Algebraic Number Fields , 2018, CiE.

[14]  Victor L. Selivanov,et al.  Computing the Solution Operators of Symmetric Hyperbolic Systems of PDE , 2009, J. Univers. Comput. Sci..

[15]  José L. Balcázar,et al.  Structural Complexity I , 1995, Texts in Theoretical Computer Science An EATCS Series.

[16]  Klaus Weihrauch,et al.  Computable Analysis: An Introduction , 2014, Texts in Theoretical Computer Science. An EATCS Series.

[17]  Zhou Jian-Ping.  On the degree of extensions generated by finitely many algebraic numbers , 1990 .