暂无分享,去创建一个
[1] S. Smale,et al. The mathematics of numerical analysis , 1996 .
[2] Colm Art O'Cinneide,et al. Relative-error bounds for the LU decomposition via the GTH algorithm , 1996 .
[3] James Demmel,et al. Accurate and Efficient Floating Point Summation , 2003, SIAM J. Sci. Comput..
[4] Dima Grigoriev,et al. Complexity Lower Bounds for Approximation Algebraic Computation Trees , 1999, J. Complex..
[5] M. Pichat,et al. Correction d'une somme en arithmetique a virgule flottante , 1972 .
[6] Olga Taussky-Todd. SOME CONCRETE ASPECTS OF HILBERT'S 17TH PROBLEM , 1996 .
[7] Alfred V. Aho,et al. The Design and Analysis of Computer Algorithms , 1974 .
[8] G. Alefeld,et al. Introduction to Interval Computation , 1983 .
[9] David H. Bailey,et al. A Fortran 90-based multiprecision system , 1995, TOMS.
[10] I. G. MacDonald,et al. Symmetric functions and Hall polynomials , 1979 .
[11] Plamen Koev,et al. Accurate SVDs of polynomial Vandermonde matrices involving orthonormal polynomials , 2006 .
[12] James Demmel,et al. The Accurate and Efficient Solution of a Totally Positive Generalized Vandermonde Linear System , 2005, SIAM J. Matrix Anal. Appl..
[13] J. Demmel. On condition numbers and the distance to the nearest ill-posed problem , 2015 .
[14] Felipe Cucker,et al. COMPLEXITY AND REAL COMPUTATION: A MANIFESTO , 1996 .
[15] Lenore Blum,et al. Computing over the Reals: Where Turing Meets Newton , 2004 .
[16] James Demmel. Underflow and the Reliability of Numerical Software , 1984 .
[17] S. Smale,et al. On a theory of computation and complexity over the real numbers; np-completeness , 1989 .
[18] Jean Vignes,et al. A stochastic arithmetic for reliable scientific computation , 1993 .
[19] Jonathan Richard Shewchuk,et al. Adaptive Precision Floating-Point Arithmetic and Fast Robust Geometric Predicates , 1997, Discret. Comput. Geom..
[20] Lenore Blum,et al. Complexity and Real Computation , 1997, Springer New York.
[21] J. Neumann,et al. Numerical inverting of matrices of high order , 1947 .
[22] Felipe Cucker,et al. Complexity estimates depending on condition and round-off error , 1998, JACM.
[23] Douglas M. Priest,et al. Algorithms for arbitrary precision floating point arithmetic , 1991, [1991] Proceedings 10th IEEE Symposium on Computer Arithmetic.
[24] James Renegar,et al. Is It Possible to Know a Problem Instance Is Ill-Posed?: Some Foundations for a General Theory of Condition Numbers , 1994, J. Complex..
[25] Froilán M. Dopico,et al. An Orthogonal High Relative Accuracy Algorithm for the Symmetric Eigenproblem , 2003, SIAM J. Matrix Anal. Appl..
[26] Xiaomei Yang. Rounding Errors in Algebraic Processes , 1964, Nature.
[27] David H. Bailey,et al. Multiprecision Translation and Execution of Fortran Programs , 1993 .
[28] James Renegar,et al. On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part III: Quantifier Elimination , 1992, J. Symb. Comput..
[29] J. Renegar,et al. On the Computational Complexity and Geometry of the First-Order Theory of the Reals, Part I , 1989 .
[30] G. Ziegler. Lectures on Polytopes , 1994 .
[31] Ramon E. Moore. Methods and applications of interval analysis , 1979, SIAM studies in applied mathematics.
[32] James Demmel,et al. Accurate SVDs of Structured Matrices , 1998 .
[33] James Demmel,et al. Accurate and Ecient Algorithms for Floating Point Computation , 2003 .
[34] Marian Boykan Pour-El,et al. Computability in analysis and physics , 1989, Perspectives in Mathematical Logic.
[35] F. Cucker,et al. Decision Problems and Round-Off Machines , 2001, Theory of Computing Systems.
[36] Plamen Koev,et al. Accurate Eigenvalues and SVDs of Totally Nonnegative Matrices , 2005, SIAM J. Matrix Anal. Appl..
[37] A. Tarski. A Decision Method for Elementary Algebra and Geometry , 2023 .
[38] Charalambos A. Charalambides,et al. Enumerative combinatorics , 2018, SIGA.
[39] James Demmel. On error analysis in arithmetic with varying relative precision , 1987, 1987 IEEE 8th Symposium on Computer Arithmetic (ARITH).
[40] I. M. Gelʹfand,et al. Discriminants, Resultants, and Multidimensional Determinants , 1994 .
[41] Qiang Ye,et al. Entrywise perturbation theory for diagonally dominant M-matrices with applications , 2002, Numerische Mathematik.
[42] Arun Ram,et al. Schur functions , 2005 .
[43] James Demmel,et al. Accurate SVDs of weakly diagonally dominant M-matrices , 2004, Numerische Mathematik.
[44] F. Olver,et al. Closure and precision in level-index arithmetic , 1990 .
[45] Nicholas J. Higham,et al. INVERSE PROBLEMS NEWSLETTER , 1991 .
[46] Chris D. Godsil,et al. ALGEBRAIC COMBINATORICS , 2013 .
[47] Joseph L. Taylor. Several Complex Variables with Connections to Algebraic Geometry and Lie Groups , 2002 .
[48] Kenneth L. Clarkson,et al. Safe and effective determinant evaluation , 1992, Proceedings., 33rd Annual Symposium on Foundations of Computer Science.
[49] James Demmel,et al. Applied Numerical Linear Algebra , 1997 .
[50] Jan Awrejcewicz,et al. Bifurcation and Chaos , 1995 .
[51] Keith Kendig. Elementary algebraic geometry , 1976 .
[52] B. Sturmfels,et al. Combinatorial Commutative Algebra , 2004 .
[53] Françoise Chaitin-Chatelin,et al. Lectures on finite precision computations , 1996, Software, environments, tools.
[54] A. Neumaier. Interval methods for systems of equations , 1990 .
[55] Daniel A. Spielman. The Smoothed Analysis of Algorithms , 2005, FCT.
[56] C. Wampler,et al. Basic Algebraic Geometry , 2005 .
[57] Nicholas J. Higham,et al. Stability analysis of algorithms for solving confluent Vandermonde-like systems , 1990 .
[58] A. Turing. ROUNDING-OFF ERRORS IN MATRIX PROCESSES , 1948 .
[59] T. J. Dekker,et al. A floating-point technique for extending the available precision , 1971 .
[61] B. Reznick. Some concrete aspects of Hilbert's 17th Problem , 2000 .
[62] J. Demmel,et al. Computing the Singular Value Decomposition with High Relative Accuracy , 1997 .
[63] Qiang Ye,et al. Accurate computation of the smallest eigenvalue of a diagonally dominant M-matrix , 2002, Math. Comput..
[64] Ker-I Ko,et al. Complexity Theory of Real Functions , 1991, Progress in Theoretical Computer Science.
[65] Erdem Hokenek,et al. Design of the IBM RISC System/6000 Floating-Point Execution Unit , 1990, IBM J. Res. Dev..
[66] Plamen Koev. Accurate Computations with Totally Nonnegative Matrices , 2007, SIAM J. Matrix Anal. Appl..
[67] James Demmel. The Complexity of Accurate Floating Point Computation , 2002 .