Topic
Multiplicative function
About: Multiplicative function is a research topic. Over the lifetime, 9058 publications have been published within this topic receiving 139416 citations. The topic is also known as: weakly multiplicative function.
Papers published on a yearly basis
1 / 2
Papers
Proceedings Article•
1 Jan 2000TL;DR: Two different multiplicative algorithms for non-negative matrix factorization are analyzed and one algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence.
Abstract: Non-negative matrix factorization (NMF) has previously been shown to be a useful decomposition for multivariate data. Two different multiplicative algorithms for NMF are analyzed. They differ only slightly in the multiplicative factor used in the update rules. One algorithm can be shown to minimize the conventional least squares error while the other minimizes the generalized Kullback-Leibler divergence. The monotonic convergence of both algorithms can be proven using an auxiliary function analogous to that used for proving convergence of the Expectation-Maximization algorithm. The algorithms can also be interpreted as diagonally rescaled gradient descent, where the rescaling factor is optimally chosen to ensure convergence.
9,013 citations
TL;DR: In this paper, the authors define rank (X) as the minimum number of triads whose sum is X, and dim1(X) to be the dimensionality of the space of matrices generated by the 1-slabs of X.
1,873 citations
1 Jan 1968
1,800 citations
Book•
1 Jan 1998
TL;DR: Approximate additive and approximately linear mappings stability of the quadratic functional equation generalizations, the method of invariant means approximately multiplicative mappings, superstability stability of functional equations for trigonometric and similar functions functions functions with bounded nth differences, stability of generalized orthogonality functional equation stability and set-valued mappings Stability of stationary and minimum points functional congruences quasi-additive functions and related topics as mentioned in this paper.
Abstract: Approximately additive and approximately linear mappings stability of the quadratic functional equation generalizations - the method of invariant means approximately multiplicative mappings - superstability stability of functional equations for trigonometric and similar functions functions with bounded nth differences approximately convex functions stability of the generalized orthogonality functional equation stability and set-valued mappings stability of stationary and minimum points functional congruences quasi-additive functions and related topics.
1,677 citations
Book•
1 Jun 1995
TL;DR: In this article, the saddle-point method was used for arithmetic progressions, and the Euler gamma function and the Riemann zeta function were used to generate arithmetic functions.
Abstract: Elementary methods Some tools from real analysis Prime numbers Arithmetic functions Average orders Sieve methods Extremal orders The method of van der Corput Diophantine approximation Complex analysis methods The Euler gamma function Generating functions: Dirichlet series Summation formulae The Riemann zeta function The prime number theorem and the Riemann hypothesis The Selberg-Delange method Two arithmetic applications Tauberian theorems Primes in arithmetic progressions Probabilistic methods Densities Limiting distributions of arithmetic functions Normal order Distribution of additive functions and mean values of multiplicative functions Friable integers The saddle-point method Integers free of small factors Bibliography Index
1,637 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2026 | 14 |
| 2025 | 587 |
| 2024 | 754 |
| 2023 | 1,304 |
| 2022 | 2,446 |
| 2021 | 650 |