Related papers: Efficient Task Graph Scheduling for Parallel QR Fa…

This paper introduces a randomized Householder QR factorization (RHQR). This factorization can be used to obtain a well conditioned basis of a vector space and thus can be employed in a variety of applications. The RHQR factorization of the…

The selection of most informative and discriminative features from high-dimensional data has been noticed as an important topic in machine learning and data engineering. Using matrix factorization-based techniques such as nonnegative matrix…

This paper focuses on solving large-scale, ill-conditioned, and overdetermined sparse least squares problems that arise from numerical partial differential equations (PDEs), mainly from the random feature method. To address these…

In this paper, we propose a new sequential quadratic semidefinite programming (SQSDP) method for solving degenerate nonlinear semidefinite programs (NSDPs), in which we produce iteration points by solving a sequence of stabilized quadratic…

Efficient quantum arithmetic operations are essential building blocks for complex quantum algorithms, yet few theoretical designs have been implemented in practical quantum programming frameworks. This paper presents the first complete…

This paper considers an explicit continuation method with the trusty time-stepping scheme and the limited-memory BFGS (L-BFGS) updating formula (Eptctr) for the linearly constrained optimization problem. At every iteration, Eptctr only…

Linear regression is a widely used technique to fit linear models and finds widespread applications across different areas such as machine learning and statistics. In most real-world scenarios, however, linear regression problems are often…

The unpivoted and pivoted Householder QR factorizations are ubiquitous in numerical linear algebra. A difficulty with pivoted Householder QR is the communication bottleneck introduced by pivoting. In this paper we propose using random…

Quantum computers are currently noisy, particularly without error correction and fault tolerance. Methods like error suppression and mitigation are widely used to improve performance. Circuit cutting, which partitions a circuit into smaller…

We develop a Sequential Quadratic Optimization (SQP) algorithm for minimizing a stochastic objective function subject to deterministic equality constraints. The method utilizes two different stepsizes, one which exclusively scales the…

In this paper, a new graph partitioning problem is introduced. The depth of each part is constrained, i.e., the node count in the longest path of the corresponding sub-graph is no more than a predetermined positive integer value p. An…

Quantum algorithms for solving problems of interesting size often result in circuits with a very large number of qubits and quantum gates. Fortunately, these algorithms also tend to contain a small number of repetitively-used quantum…

This paper considers the regularization continuation method and the trust-region updating strategy for the nonlinearly equality-constrained optimization problem. Namely, it uses the inverse of the regularization quasi-Newton matrix as the…

Convex regression (CR) problem deals with fitting a convex function to a finite number of observations. It has many applications in various disciplines, such as statistics, economics, operations research, and electrical engineering.…

Maximum likelihood estimation of mixture proportions has a long history, and continues to play an important role in modern statistics, including in development of nonparametric empirical Bayes methods. Maximum likelihood of mixture…

We present LQR-CBF-RRT*, an incremental sampling-based algorithm for offline motion planning. Our framework leverages the strength of Control Barrier Functions (CBFs) and Linear Quadratic Regulators (LQR) to generate safety-critical and…

Complex Query Answering (CQA) is an important and fundamental task for knowledge graph (KG) reasoning. Query encoding (QE) is proposed as a fast and robust solution to CQA. In the encoding process, most existing QE methods first parse the…

The Cholesky QR algorithm is an efficient communication-minimizing algorithm for computing the QR factorization of a tall-skinny matrix. Unfortunately it has the inherent numerical instability and breakdown when the matrix is…

The efficient parallel execution of complex computations requires balancing the workload across processors while minimizing the communication between them. This inherent trade-off is often captured by graph partitioning or DAG scheduling…

This paper presents a unified framework that connects sequential quadratic programming (SQP) and the iterative linear-parameter-varying model predictive control (LPV-MPC) technique. Using the differential formulation of the LPV-MPC, we…