Parallel Cholesky-based reduction for the weighted integer least squares problem

Reduction in Solving Some Integer Least Squares Problems

Solving an integer least squares (ILS) problem usually consists of two stages: reduction and search. This thesis is concerned with the reduction process for the ordinary ILS problem and the ellipsoid-constrained ILS problem. For the ordinary ILS problem, we dispel common misconceptions on the reduction stage in the literature and show what is crucial to the efficiency of the search process. The...

FPGA Based Efficient Cholesky Decomposition for Solving Least Square Problem

The paper presents FPGA based design & implementation of Cholesky Decomposition for matrix calculation to solve least square problem. The Cholesky decomposition has no pivoting but the factorization is stable. It also has an advantage that instead of two matrices, only one matrix multiplied by itself. Hence it requires two times less operation. The Cholesky decomposition has been designed & sim...

The element-wise weighted total least-squares problem

A new technique is considered for parameter estimation in a linear measurement error model AX ≈ B, A=A0 + Ã, B=B0 + B̃, A0X0 =B0 with row-wise independent and non-identically distributed measurement errors Ã, B̃. Here, A0 and B0 are the true values of the measurements A and B, and X0 is the true value of the parameter X. The total least-squares method yields an inconsistent estimate of the parame...

Parallel Nonnegative Least Squares Solvers for Model Order Reduction

Resurrecting Weighted Least Squares

This paper shows how asymptotically valid inference in regression models based on the weighted least squares (WLS) estimator can be obtained even when the model for reweighting the data is misspecified. Like the ordinary least squares estimator, the WLS estimator can be accompanied by heterokedasticty-consistent (HC) standard errors without knowledge of the functional form of conditional hetero...