A generalized worst-case complexity analysis for non-monotone line searches

AbstractWe present abstract complexity results about Coquand and Hyland–Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical process game semantics can model and apply to. In particular, we provide a novel method to bound the length of interactions between visible strategies and to measure precisely the tower of exponentials defining the worst-case complexity. Our study improves the old estimates on average by several exponentials.

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Worst-case complexity analysis of methods for logic query implementation

Proceedings of the sixth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems - PODS '87 ◽

10.1145/28659.28691 ◽

1987 ◽

Cited By ~ 18

Author(s):

A. Marchetti-Spaccamella ◽

A. Pelaggi ◽

D. Sacca

Keyword(s):

Complexity Analysis ◽

Worst Case ◽

Case Complexity ◽

Worst Case Complexity

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Better Worst-Case Complexity Analysis of the Block Coordinate Descent Method for Large Scale Machine Learning

2017 16th IEEE International Conference on Machine Learning and Applications (ICMLA) ◽

10.1109/icmla.2017.00-43 ◽

2017 ◽

Author(s):

Ziqiang Shi ◽

Rujie Liu

Keyword(s):

Machine Learning ◽

Large Scale ◽

Complexity Analysis ◽

Descent Method ◽

Block Coordinate Descent ◽

Worst Case ◽

Coordinate Descent Method ◽

Case Complexity ◽

Block Coordinate Descent Method ◽

Worst Case Complexity

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Computing Minimal Polynomials of Matrices

LMS Journal of Computation and Mathematics ◽

10.1112/s1461157000000590 ◽

2008 ◽

Vol 11 ◽

pp. 252-279 ◽

Cited By ~ 4

Author(s):

Max Neunhöffer ◽

Cheryl E. Praeger

Keyword(s):

Monte Carlo ◽

Finite Field ◽

Minimal Polynomial ◽

Complexity Analysis ◽

Monte Carlo Algorithm ◽

Practical Implementation ◽

Worst Case ◽

Case Complexity ◽

Matrix Operations ◽

Worst Case Complexity

AbstractWe present and analyse a Monte-Carlo algorithm to compute the minimal polynomial of ann × nmatrix over a finite field that requiresO(n3) field operations andO(n) random vectors, and is well suited for successful practical implementation. The algorithm, and its complexity analysis, use standard algorithms for polynomial and matrix operations. We compare features of the algorithm with several other algorithms in the literature. In addition we present a deterministic verification procedure which is similarly efficient in most cases but has a worst-case complexity ofO(n4). Finally, we report the results of practical experiments with an implementation of our algorithms in comparison with the current algorithms in the GAP library.

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