Solving Least Squares Problems

  title={Solving Least Squares Problems},
  author={Ake Bjork and Charles L. Lawson and Richard J. Hanson},
  journal={Mathematics of Computation},
New Numerical Algorithm for Deflation of Infinite and Zero Eigenvalues and Full Solution of Quadratic Eigenvalue Problems
A new method for computing all eigenvalues and eigenvectors of quadratic matrix pencil Q(λ)=λ2 M + λ C + K so that careful preprocessing allows scaling invariant/component-wise backward error and thus a better condition number.
Prony, Pad\'e, and Linear Prediction for Interpolation and Approximation in the Time and Frequency Domain Design of IIR Digital Filters and in Parameter Identification
This note examines model based signal processing, signal analysis or signal representation, and linear prediction with the goal of showing they are all based on the same principles and all can be extended and generalized.
A Gradient-thresholding Algorithm for Sparse Regularization
This paper proposes a new (semi-) iterative regularization method which is not only simpler than the mentioned algorithms but also yields better results, in terms of accuracy and sparsity of the recovered solution.
Wireless link modeling using complex FIR filters
  • M. Dadic, R. Zentner
  • Engineering
    2018 First International Colloquium on Smart Grid Metrology (SmaGriMet)
  • 2018
This paper presents a method for wireless link modeling, based on complex coefficient finite-impulse-response (FIR) digital filters, which allows easy, unconstrained least-squares estimation of the target transfer function in the frequency domain, which is performed using the Moore-Penrose matrix pseudoinverse.
How many faces can be recognized? Performance extrapolation for multi-class classification
It is shown that the expected accuracy when the classifier is trained on $k$ classes is the k-1 moment of a conditional accuracy distribution, which can be estimated from data.
Point and beam-sparse radio astronomical source recovery using non-negative least squares
A simple and novel algorithm for source recovery based on array data measurements in radio astronomy is proposed, and it is shown that the sparsity promoted by the NNLS algorithm results in a super-resolution estimate for the point sources and smooth recovery for the extended emissions.
Anti-lopsided Algorithm for Large-scale Nonnegative Least Square Problems
The main idea of the algorithm is to transform the original NNLS into an equivalent non-negative quadratic programming, which significantly reduce the scaling problem of variables, and can reach high accuracy and fast speed with linear convergence.
Modelling and identification of a six axes industrial robot
This paper deals with the modelling and identification of a six axes industrial St ¨aubli RX90 robot. A non-linear finite element method is used to generate the dynamic equations of motion in a form