Alan Turing and the other theory of computation (expanded)

[1]  M. Shub Mysteries of mathematics and computation , 1994 .

[2]  A. Householder A Class of Methods for Inverting Matrices , 1958 .

[3]  S. Smale,et al.  On a theory of computation and complexity over the real numbers; np-completeness , 1989 .

[4]  James Hardy Wilkinson,et al.  Some Comments from a Numerical Analyst , 1971, JACM.

[5]  S. Smale The fundamental theorem of algebra and complexity theory , 1981 .

[6]  Steve Smale,et al.  Complexity theory and numerical analysis , 1997, Acta Numerica.

[7]  Carlos Beltrán,et al.  Fast Linear Homotopy to Find Approximate Zeros of Polynomial Systems , 2011, Found. Comput. Math..

[8]  John von Neumann The Principles of Large-Scale Computing Machines , 1981, IEEE Ann. Hist. Comput..

[9]  J. Demmel On condition numbers and the distance to the nearest ill-posed problem , 2015 .

[10]  Lenore Blum,et al.  Computing over the Reals: Where Turing Meets Newton , 2004 .

[11]  Peter Bürgisser,et al.  Smoothed Analysis of Condition Numbers , 2011 .

[12]  Stephen Smale,et al.  Complexity of Bezout's Theorem V: Polynomial Time , 1994, Theor. Comput. Sci..

[13]  J. Neumann,et al.  Numerical inverting of matrices of high order , 1947 .

[14]  Andrew Hodges,et al.  Alan Turing: The Enigma , 1983 .

[15]  G. Dantzig Origins of the simplex method , 1990 .

[16]  James Renegar,et al.  A faster PSPACE algorithm for deciding the existential theory of the reals , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[17]  E. Kostlan Complexity theory of numerical linear algebra , 1988 .

[18]  Felipe Cucker,et al.  Algebraic Settings for the Problem “P ≠ NP?” , 1998 .

[19]  H. Weyl On the Volume of Tubes , 1939 .

[20]  Michael Shub,et al.  Complexity of Bezout’s Theorem VII: Distance Estimates in the Condition Metric , 2009, Found. Comput. Math..

[21]  H. D. Huskey,et al.  NOTES ON THE SOLUTION OF ALGEBRAIC LINEAR SIMULTANEOUS EQUATIONS , 1948 .

[22]  C. Eckart,et al.  The approximation of one matrix by another of lower rank , 1936 .

[23]  Marian Boykan Pour-El,et al.  Computability in analysis and physics , 1989, Perspectives in Mathematical Logic.

[24]  Lenore Blum,et al.  Complexity and Real Computation , 1997, Springer New York.

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

[26]  Philipp Birken,et al.  Numerical Linear Algebra , 2011, Encyclopedia of Parallel Computing.

[27]  James Hardy Wilkinson,et al.  Rounding errors in algebraic processes , 1964, IFIP Congress.

[28]  Nicholas J. Higham,et al.  INVERSE PROBLEMS NEWSLETTER , 1991 .

[29]  Michael Shub,et al.  The complexity and geometry of numerically solving polynomial systems , 2012, 1211.1528.

[30]  H. Hotelling Some New Methods in Matrix Calculation , 1943 .

[31]  L. Santaló Integral geometry and geometric probability , 1976 .

[32]  Felipe Cucker,et al.  Separation of Complexity Classes in Koiran's Weak Model , 1994, Theor. Comput. Sci..

[33]  James Renegar,et al.  Incorporating Condition Measures into the Complexity Theory of Linear Programming , 1995, SIAM J. Optim..

[34]  James Renegar,et al.  A polynomial-time algorithm, based on Newton's method, for linear programming , 1988, Math. Program..

[35]  D. Spielman,et al.  Smoothed analysis of algorithms: Why the simplex algorithm usually takes polynomial time , 2004 .

[36]  A. Tarski A Decision Method for Elementary Algebra and Geometry , 2023 .

[37]  A. Edelman Eigenvalues and condition numbers of random matrices , 1988 .

[38]  H. Fédérer Geometric Measure Theory , 1969 .

[39]  Felipe Cucker,et al.  On a problem posed by Steve Smale , 2009, 0909.2114.

[40]  Felipe Cucker Real Computations with Fake Numbers , 1999, ICALP.

[41]  A. Turing On Computable Numbers, with an Application to the Entscheidungsproblem. , 1937 .

[42]  Casiano Rodríguez León,et al.  Alan Mathison Turing , 2000 .

[43]  J. Todd,et al.  The condition of a certain matrix , 1950, Mathematical Proceedings of the Cambridge Philosophical Society.

[44]  Joseph F. Grcar,et al.  John von Neumann's Analysis of Gaussian Elimination and the Origins of Modern Numerical Analysis , 2011, SIAM Rev..

[45]  S. Smale Mathematical problems for the next century , 1998 .

[46]  V. Klee,et al.  HOW GOOD IS THE SIMPLEX ALGORITHM , 1970 .

[47]  D. Spielman,et al.  Smoothed Analysis of Renegar’s Condition Number for Linear Programming , 2002 .

[48]  James Renegar,et al.  Linear programming, complexity theory and elementary functional analysis , 1995, Math. Program..

[49]  Lenore Blum,et al.  Alan turing and the other theory of computation , 2012, ITiCSE '12.