Using Interval Analysis to Bound Numerical Errors in Scientific Computing
暂无分享,去创建一个
[1] R. Beatson,et al. A short course on fast multipole methods , 1997 .
[2] Siegfried M. Rump,et al. Accurate Sum and Dot Product , 2005, SIAM J. Sci. Comput..
[3] L. Greengard,et al. Regular Article: A Fast Adaptive Multipole Algorithm in Three Dimensions , 1999 .
[4] L. Greengard,et al. A new version of the Fast Multipole Method for the Laplace equation in three dimensions , 1997, Acta Numerica.
[5] Michael J. Schulte,et al. The Interval-Enhanced GNU Fortran Compiler , 1999, Reliab. Comput..
[6] Don Coppersmith,et al. Matrix multiplication via arithmetic progressions , 1987, STOC.
[7] Yozo Hida,et al. Accurate Floating Point Summation , 2002 .
[8] Rajat P. Garg,et al. Techniques for Optimizing Applications: High Performance Computing , 2001 .
[9] Intel Corportation,et al. IA-32 Intel Architecture Software Developers Manual , 2004 .
[10] George T. Gillies,et al. The Newtonian gravitational constant: recent measurements and related studies , 1997 .
[11] S. Gill,et al. A process for the step-by-step integration of differential equations in an automatic digital computing machine , 1951, Mathematical Proceedings of the Cambridge Philosophical Society.
[12] Tiraz R. Birdie,et al. The Use of Interval Analysis in Hydrologic Systems , 1998, Reliab. Comput..
[13] Jack M. Wolfe. Reducing truncation errors by programming , 1964, CACM.
[14] Walter Krämer,et al. Automatic Forward Error Analysis for Floating Point Algorithms , 2001, Reliab. Comput..
[15] Charles Fefferman,et al. Interval Arithmetic in Quantum Mechanics , 1996 .
[16] Nobito Yamamoto,et al. A Numerical Verification of Nontrivial Solutions for the Heat Convection Problem , 2004 .
[17] Martin Head-Gordon,et al. Derivation and efficient implementation of the fast multipole method , 1994 .
[18] Eldon Hansen,et al. Global optimization using interval analysis , 1992, Pure and applied mathematics.
[19] John Michael McNamee,et al. A comparison of methods for accurate summation , 2004, SIGS.
[20] Svetoslav Markov,et al. On the algebraic Properties of Stochastic Arithmetic. Comparison to Interval Arithmetic , 2001 .
[21] U. Kulisch,et al. Scientific Computing with Automatic Result Verification. , 1994 .
[22] Richard Goodman,et al. Convergence Estimates for the Distribution of Trailing Digits , 1976, JACM.
[23] J. Vignes,et al. An Efficient Stochastic Method for Round-Off Error Analysis , 1985, Accurate Scientific Computations.
[24] Martin Berz,et al. Efficient Control of the Dependency Problem Based on Taylor Model Methods , 1999, Reliab. Comput..
[25] J. Hass,et al. The double bubble conjecture , 1995 .
[26] Bruno Lang,et al. Newton's constant of gravitation and verified numerical quadrature , 1996, Reliab. Comput..
[27] Leslie Greengard,et al. A fast algorithm for particle simulations , 1987 .
[28] V. Strassen. Gaussian elimination is not optimal , 1969 .
[29] Mark A. Stadtherr,et al. ROBUST PHASE STABILITY ANALYSIS USING INTERVAL METHODS , 1998 .
[30] Charles L. Lawson,et al. Basic Linear Algebra Subprograms for Fortran Usage , 1979, TOMS.
[31] Arnold Neumaier,et al. Taylor Forms—Use and Limits , 2003, Reliab. Comput..
[32] David L. Weaver,et al. The SPARC Architecture Manual , 2003 .
[33] Guido D. Salvucci,et al. Ieee standard for binary floating-point arithmetic , 1985 .
[34] David L Weaver,et al. The SPARC architecture manual : version 9 , 1994 .
[35] C. Fefferman,et al. Aperiodicity of the Hamiltonian flow in the Thomas-Fermi potential. , 1993 .
[36] Y. Lin,et al. Advances in Interval Methods for Deterministic Global Optimization in Chemical Engineering , 2004, J. Glob. Optim..
[37] Jack J. Dongarra,et al. An extended set of FORTRAN basic linear algebra subprograms , 1988, TOMS.
[38] Jon G. Rokne,et al. Complex interval arithmetic , 1971, CACM.
[39] Don Coppersmith,et al. Matrix multiplication via arithmetic progressions , 1987, STOC.
[40] Martin Berz,et al. Controlling the Wrapping Effect in the Solution of ODEs for Asteroids , 2003, Reliab. Comput..
[41] Michael J. Schulte,et al. A combined interval and floating point multiplier , 1998, Proceedings of the 8th Great Lakes Symposium on VLSI (Cat. No.98TB100222).
[42] Nicholas J. Higham,et al. INVERSE PROBLEMS NEWSLETTER , 1991 .
[43] Ulrich W. Kulisch,et al. Proposal for Accurate Floating-Point Vector Arithmetic , 1993 .
[44] Eldon R. Hansen,et al. Sharpness in Interval Computations , 1997, Reliab. Comput..
[45] Arnold Neumaier,et al. Grand Challenges and Scientific Standards in Interval Analysis , 2002, Reliab. Comput..
[46] Ole Møller. Quasi double-precision in floating point addition , 1965 .
[47] William Kahan,et al. Pracniques: further remarks on reducing truncation errors , 1965, CACM.
[48] Michael A. Malcolm,et al. On accurate floating-point summation , 1971, CACM.