arXiv Open Access 2023

Sharp inequality for $\ell_p$ quasi-norm and $\ell_q$-norm with $0<p\leq 1$ and $q>1$

Zenghui Zhang

Lihat Sumber

Abstrak

A sharp inequality for $\ell_p$ quasi-norm with $0<p\leq 1$ and $\ell_q$-norm with $q>1$ is derived, which shows that the difference between $\|\textbf{\textit{x}}\|_p$ and $\|\textbf{\textit{x}}\|_q$ of an $n$-dimensional signal $\textbf{\textit{x}}$ is upper bounded by the difference between the maximum and minimum absolute value in $\textbf{\textit{x}}$. The inequality could be used to develop new $\ell_p$-minimization algorithms.

Topik & Kata Kunci

eess.SP

Penulis (1)

Zenghui Zhang

Format Sitasi

APA MLA BibTeX

Zhang, Z. (2023). Sharp inequality for $\ell_p$ quasi-norm and $\ell_q$-norm with $0<p\leq 1$ and $q>1$. https://arxiv.org/abs/2312.16394

Akses Cepat

Lihat di Sumber

Informasi Jurnal

Tahun Terbit: 2023
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓