A Low-Rank Algorithm for Weakly Compressible Flow

A Two -Step Modification toward Implementing Compressible Source Terms in Low Compressible Flows

periodic unsteady transonic compressible flow simulation using fourier-based algorithm

the present research simulates time-periodic unsteady transonic flow around pitching airfoils via the solution of unsteady euler and navier-stokes equations, using time spectral method (tsm) and compares it with the traditional methods such as bdf and explicit structured adaptive grid method. the tsm uses a fourier representation in time and hence solves for the periodic state directly accordin...

A Hierarchical Singular Value Decomposition Algorithm for Low Rank Matrices

Singular value decomposition (SVD) is a widely used technique for dimensionality reduction and computation of basis vectors. In many applications, especially in fluid mechanics, the matrices are dense, but low-rank matrices. In these cases, a truncated SVD corresponding to the most significant singular values is sufficient. In this paper, we propose a tree based merge-and-truncate algorithm to ...

A Fast Augmented Lagrangian Algorithm for Learning Low-Rank Matrices

We propose a general and efficient algorithm for learning low-rank matrices. The proposed algorithm converges super-linearly and can keep the matrix to be learned in a compact factorized representation without the need of specifying the rank beforehand. Moreover, we show that the framework can be easily generalized to the problem of learning multiple matrices and general spectral regularization...

A Quadratically Convergent Algorithm for Structured Low-Rank Approximation

Structured Low-Rank Approximation is a problem arising in a wide range of applications in Numerical Analysis and Engineering Sciences. Given an input matrix M , the goal is to compute a matrix M ′ of given rank r in a linear or affine subspace E of matrices (usually encoding a specific structure) such that the Frobenius distance ‖M −M ′‖ is small. We propose a Newton-like iteration for solving ...