Publications related to A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

We propose new algorithms to overcome two of the most constraining limitations of surface reconstruction methods in use. In particular, we focus on the large amount of data characterizing standard acquisitions by scanner and the noise intrinsically introdu ...

Elsevier Science Bv2017

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

Stefano Massei

We consider the problem of efficiently solving Sylvester and Lyapunov equations of medium and large scale, in case of rank-structured data, i.e., when the coefficient matrices and the right-hand side have low-rank off- diagonal blocks. This comprises probl ...

MATHICSE2017

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

We consider design of sparse controllers for a stochastic linear system with infinite horizon quadratic objective. We formulate the non-sparse optimal solution through a semidefinite program for the second order moments of the states and inputs. Given that ...

University of Minnesota2016

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

Petar Sirkovic

The focus of this thesis is on developing efficient algorithms for two important problems arising in model reduction, estimation of the smallest eigenvalue for a parameter-dependent Hermitian matrix and solving large-scale linear matrix equations, by extra ...

EPFL2016

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Afsaneh Asaei, Mohammadjavad Taghizadeh, Saeid Haghighatshoar

In this paper, we prove a new identity for the least-square solution of an over-determined set of linear equation

Ax=b

, where

A

is an

m\times n

full-rank matrix,

b

is a column-vector of dimension

m

, and

m

(the number of equations) is larger tha ...

Idiap2015

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate functions based on random sampling according to a given probability measure. Recent work has shown that ...

2015

Truncated low-rank methods for solving general linear matrix equations

Daniel Kressner, Petar Sirkovic

This work is concerned with the numerical solution of large-scale linear matrix equations A1XB1T++AKXBKT=C. The most straightforward approach computes XRmxn from the solution of an mn x mn linear system, typically limiting the feasible values of m,n to a f ...

Wiley-Blackwell2015

From averaging to acceleration, there is only a step-size

Nicolas Henri Bernard Flammarion

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present the first algorithm that a ...

2015

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Fabio Nobile, Giovanni Migliorati

Motivated by the numerical treatment of parametric and stochastic PDEs, we analyze the least-squares method for polynomial approximation of multivariate func- tions based on random sampling according to a given probability measure. Recent work has shown th ...

MATHICSE2014

Randomized Extended Kaczmarz For Solving Least Squares

Nikolaos Freris

We present a randomized iterative algorithm that exponentially converges in the mean square to the minimum l(2)-norm least squares solution of a given linear system of equations. The expected number of arithmetic operations required to obtain an estimate o ...

Society for Industrial and Applied Mathematics2013

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Graph Chatbot

Chat with Graph Search

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

Truncated low-rank methods for solving general linear matrix equations

From averaging to acceleration, there is only a step-size

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

Randomized Extended Kaczmarz For Solving Least Squares

Low-rank methods for parameter-dependent eigenvalue problems and matrix equations

MATHICSE Technical Report : Solving rank structured Sylvester and Lyapunov equations

Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs

‪Stochastic Control-A Moment Approach to Sparse Control Design‬

MATHICSE Technical Report : Discrete least squares polynomial approximation with random evaluations – application to parametric and stochastic elliptic PDES

From averaging to acceleration, there is only a step-size

Randomized Extended Kaczmarz For Solving Least Squares

Reconstruction of 3D scattered data via radial basis functions by efficient and robust techniques

A New Identity for the Least-square Solution of Overdetermined Set of Linear Equations

Truncated low-rank methods for solving general linear matrix equations