6 papers
Approximate Inversion of Discrete Fourier Integral Operators via Hierarchically Semiseparable Matrices
Yingzhou Li, Jingyu Liu
This paper introduces a novel method for approximating the inverse of discrete Fourier integral operators (FIOs). Given an matrix representation of an FIO, the pro…
A Superfast Direct Solver for 2D Type-II Inverse Nonuniform Discrete Fourier Transform Based on Hierarchically Semiseparable Matrices
Yingzhou Li, Jingyu Liu
Reconstructing images on Cartesian grids from nonuniform Fourier samples is a basic computational task in Fourier reconstruction methods for computed tomography. This paper propose…
A Superfast Direct Solver for Type-III Inverse Nonuniform Discrete Fourier Transform
Yingzhou Li, Jingyu Liu
The nonuniform discrete Fourier transform (NUDFT) and its inverse are widely used in various fields of scientific computing. In this article, we propose a novel superfast direct in…
Products between block-encodings
Dekuan Dong, Yingzhou Li, Jungong Xue
Block-encoding is a standard framework for embedding matrices into unitary operators in quantum algorithms. Efficient implementation of products between block-encoded matrices is c…
Hierarchical Tucker Low-Rank Matrices: Construction and Matrix-Vector Multiplication
Yingzhou Li, Jingyu Liu
In this paper, a hierarchical Tucker low-rank (HTLR) matrix is proposed to approximate non-oscillatory kernel functions in linear complexity. The HTLR matrix is based on the hierar…
A Model-Based Derivative-Free Optimization Algorithm for Partially Separable Problems
Yichuan Liu, Yingzhou Li
We propose UPOQA, a derivative-free optimization algorithm for partially separable unconstrained problems, leveraging quadratic interpolation and a structured trust-region framewor…