Haibo Li

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math.NA2026

Data-informed posterior approximation for Bayesian linear inverse problems

Haibo Li

Computing posterior distributions in large-scale Bayesian linear inverse problems is challenging due to the high dimensionality of the parameter space. In this work, we develop a d…

math.NA2025

Krylov iterative methods for linear least squares problems with linear equality constraints

Haibo Li

We consider the linear least squares problem with linear equality constraints (LSE problem) formulated as $min_{x \in R^{n}} ∥ A x - b ∥_{2} s.t. C x = d$ . Although t…

math.NA2024

A new interpretation of the weighted pseudoinverse and its applications

Haibo Li

Consider the generalized linear least squares (GLS) problem $min ∥ Lx ∥_{2} s.t. ∥ M (A x - b) ∥_{2} = min$ . The weighted pseudoinverse $A_{M L}^{a^} $ is the matrix that maps $b$ …

math.NA2024

Characterizing GSVD by singular value expansion of linear operators and its computation

Haibo Li

The generalized singular value decomposition (GSVD) of a matrix pair ${A, L}$ with $A \in R^{m \times n}$ and $L \in R^{p \times n}$ generalizes the singular value de…