Fetching the paper…
Reading the bibliography…
We survey key techniques and results from approximation theory in the context of uniform approximations to real functions such as e^{-x}, 1/x, and x^k.
Lecons sur les Fonctions de Variables Réelles et les Développements en Séries de Polynomes
Émile Borel · 1905
Earlier work this paper cites.
Orthogonal polynomials
Gabor Szego · 1939
Earlier work this paper cites.
Methods of Conjugate Gradients for solving linear systems
Magnus R. Hestenes and Eduard Stiefel · 1952
Earlier work this paper cites.
Solution of systems of linear equations by minimized iterations
Cornelius Lanczos · 1952
Earlier work this paper cites.
Handbook of Mathematical Functions
M. Abramowitz and I.A. Stegun · 1964
Earlier work this paper cites.
Rational approximation to | x | |x|
Donald J. Newman · 1964
Earlier work this paper cites.
Introduction to approximation theory
E. W. Cheney · 1966
Earlier work this paper cites.
Estimates for some computational techniques in linear algebra
Shmuel Kaniel · 1966
Earlier work this paper cites.
Chebyshev rational approximations to e − x e^{-x} in [ 0 , ∞ ) [0,\infty) and applications to heat-conduction problems
W.J Cody, G Meinardus, and R.S Varga · 1969
Earlier work this paper cites.
An introduction to the approximation of functions
T.J. Rivlin · 1969
Earlier work this paper cites.
A lower bound for the smallest eigenvalue of the Laplacian
J. Cheeger · 1970
Earlier work this paper cites.
Zur rationalen Approximierbarkeit von e − x e^{-x} über [ 0 , ∞ ) [0,\infty)
A Schönhage · 1973
Earlier work this paper cites.
Rational approximation to e − x e^{-x}
Donald J. Newman · 1974
Earlier work this paper cites.
Geometric convergence to e − z e^{-z} by rational functions with real poles
E. B. Saff, A. Schönhage, and R. S. Varga · 1975
Earlier work this paper cites.
Principles of mathematical analysis
Walter Rudin · 1976
Earlier work this paper cites.
The symmetric eigenvalue problem
Beresford N Parlett · 1980
Earlier work this paper cites.
On the rates of convergence of the Lanczos and the block-Lanczos methods
Y. Saad · 1980
Earlier work this paper cites.
Approximation of e − x e^{-x} by rational functions with concentrated negative poles
Jan-Erik Andersson · 1981
Earlier work this paper cites.
On convergence of simultaneous Padé approximants for systems of functions of Markov type
A.A. Gonchar and E.A. Rakhmanov · 1983
Earlier work this paper cites.
λ 1 \lambda_{1} , isoperimetric inequalities for graphs, and superconcentrators
Noga Alon and V. D. Milman · 1985
Earlier work this paper cites.
Conductance and convergence of Markov chains-A combinatorial treatment of expanders
Milena Mihail · 1989
Cited alongside, same era.
Estimating the largest eigenvalues by the power and Lanczos algorithms with a random start
J. Kuczyński and H. Woźniakowski · 1992
Cited alongside, same era.
Concrete Mathematics: A Foundation for Computer Science
Ronald L. Graham, Donald E. Knuth, and Oren Patashnik · 1994
Cited alongside, same era.
On the degree of Boolean functions as real polynomials
Noam Nisan and Mario Szegedy · 1994
Cited alongside, same era.
PP is closed under intersection
R. Beigel, N. Reingold, and D. Spielman · 1995
Cited alongside, same era.
A fast quantum mechanical algorithm for database search
Lov K. Grover · 1996
Cited alongside, same era.
On partitioning graphs via single commodity flows
Lorenzo Orecchia, Leonard J. Schulman, Umesh V. Vazirani, and Nisheeth K. Vishnoi · 2008
Later among the works it cites.
Two-message quantum interactive proofs are in PSPACE
Rahul Jain, Sarvagya Upadhyay, and John Watrous · 2009
Later among the works it cites.
Parallel approximation of non-interactive zero-sum quantum games
Rahul Jain and John Watrous · 2009
Later among the works it cites.
On the computation of the exponential integral
N.N. Kalitkin and I.A. Panin · 2009
Later among the works it cites.
Breaking the multicommodity flow barrier for O ( log n ) {O}(\sqrt{\log n}) -approximations to Sparsest Cut
Jonah Sherman · 2009
Later among the works it cites.
Lower bounds in communication complexity and learning theory via analytic methods
Alexander Sherstov · 2009
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Über eine Eigenschaft der Exponentialreihe
G. Szegö · 1996
Cited alongside, same era.
Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92)
Fan R.K. Chung · 1997
Cited alongside, same era.
On Krylov subspace approximations to the matrix exponential operator
Marlis Hochbruck and Christian Lubich · 1997
Cited alongside, same era.
The complexity of the matrix eigenproblem
Victor Y. Pan and Zhao Q. Chen · 1999
Cited alongside, same era.
Iterative solution of linear systems in the 20th century
Yousef Saad and Henk A. van der Vorst · 2000
Cited alongside, same era.
Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
Cited alongside, same era.
Later among the works it cites.
Approximation by exponential sums revisited
Gregory Beylkin and Lucas Monzón · 2010
Later among the works it cites.
QIP = = PSPACE
Rahul Jain, Zhengfeng Ji, Sarvagya Upadhyay, and John Watrous · 2011
Later among the works it cites.
A nearly- m log n m\log n time solver for SDD linear systems
Ioannis Koutis, Gary L. Miller, and Richard Peng · 2011
Later among the works it cites.
Fast Approximation Algorithms for Graph Partitioning using Spectral and Semidefinite-Programming Techniques
Lorenzo Orecchia · 2011
Later among the works it cites.
Lorenzo Orecchia, Sushant Sachdeva, and Nisheeth K. Vishnoi · 2011
Later among the works it cites.
Towards an SDP-based approach to spectral methods: A nearly-linear-time algorithm for graph partitioning and decomposition
Lorenzo Orecchia and Nisheeth K. Vishnoi · 2011
Later among the works it cites.
Numerical methods for large eigenvalue problems
Yousef Saad · 2011
Later among the works it cites.
The multiplicative weights update method: a meta-algorithm and applications
Sanjeev Arora, Elad Hazan, and Satyen Kale · 2012
Later among the works it cites.
Approximating the exponential, the Lanczos method and an O ~ \widetilde{O} (m)-time spectral algorithm for Balanced Separator
Lorenzo Orecchia, Sushant Sachdeva, and Nisheeth K. Vishnoi · 2012
Later among the works it cites.
L x = b {L}x=b
Nisheeth K Vishnoi · 2012
Later among the works it cites.
Dual lower bounds for approximate degree and Markov-Bernstein inequalities
Mark Bun and Justin Thaler · 2013
Closest in time.
A simple, combinatorial algorithm for solving SDD systems in nearly-linear time
Jonathan A. Kelner, Lorenzo Orecchia, Aaron Sidford, and Zeyuan Allen Zhu · 2013
Closest in time.
Matrix inversion is as easy as exponentiation
S. Sachdeva and N K. Vishnoi · 2013
Closest in time.
Nearly maximum flows in nearly linear time
Jonah Sherman · 2013
Closest in time.