How to multiply matrices faster
How to multiply matrices faster
Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable
ACM Transactions on Mathematical Software (TOMS)
A Uniform Approach for the Fast Computation of Matrix-Type Pade Approximants
SIAM Journal on Matrix Analysis and Applications
The singular value decomposition for polynomial systems
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Approximate polynomial greatest common divisors and nearest singular polynomials
ISSAC '96 Proceedings of the 1996 international symposium on Symbolic and algebraic computation
Journal of Symbolic Computation - Special issue: validated numerical methods and computer algebra
Fast evaluation of holonomic functions
Theoretical Computer Science - Special issue on real numbers and computers
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Journal of Symbolic Computation
Modern Computer Algebra
A note on algebraic independence of logarithmic and exponential constants
ACM SIGSAM Bulletin
Journal of Symbolic Computation
Multiplying matrices faster than coppersmith-winograd
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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Given d complex numbers z"1,...,z"d, it is classical that linear dependencies @l"1z"1+...+@l"dz"d=0 with @l"1,...,@l"d@?Z can be guessed using the LLL-algorithm. Similarly, given d formal power series f"1,...,f"d@?C[[z]], algorithms for computing Pade-Hermite forms provide a way to guess relations P"1f"1+...+P"df"d=0 with P"1,...,P"d@?C[z]. Assuming that f"1,...,f"d have a radius of convergence r0 and given a real number Rr, we will describe a new algorithm for guessing linear dependencies of the form g"1f"1+...+g"df"d=h, where g"1,...,g"d,h@?C[[z]] have a radius of convergence =R. We will also present two alternative algorithms for the special cases of algebraic and Fuchsian dependencies.