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2 edition of Subroutine package for processing large, sparse, least-squares problems found in the catalog.

Subroutine package for processing large, sparse, least-squares problems

William H Dillinger

# Subroutine package for processing large, sparse, least-squares problems

## by William H Dillinger

Subjects:
• Least squares -- Computer programs

• Edition Notes

The Physical Object ID Numbers Statement William H. Dillinger Series NOAA technical memorandum NOS NGS -- 29 Contributions National Geodetic Survey (U.S.) Pagination 18 p. : Number of Pages 18 Open Library OL14851235M

A linear loss function gives a standard least-squares problem. Additionally, constraints in a form of lower and upper bounds on some of $$x_j$$ are allowed. All methods specific to least-squares minimization utilize a $$m \times n$$ matrix of partial derivatives called Jacobian and defined as . ‘lsmr’ is suitable for problems with sparse and large Jacobian matrices. It uses the iterative procedure for finding a solution of a linear least-squares problem and only requires matrix-vector product evaluations. If None (default) the solver is chosen based on the type of Jacobian returned on the first iteration.

Least squares problem with large matrix. Learn more about inverse problem, least squares, large matrices. Linear least-squares solver with bounds or linear constraints. lsqlin applies only to the solver-based approach. For a discussion of the two optimization approaches, see First Choose Problem-Based or Solver-Based Approach. x = lsqlin (C,d,A,b) solves the linear system C*x = d in the least-squares sense, subject to A*x ≤ : Matrix for linear equality constraints.

Large-Scale ℓ1-Regularized Least Squares Problems Kwangmoo Koh [email protected] Seungjean Kim [email protected] Stephen Boyd [email protected] l1ls solves ℓ1-regularized least squares problems (LSPs) using the truncated Newton interior-point method described in [KKL+07]. 1 The problems l1lssolves an optimization problem of File Size: 81KB. Packages of Subroutines for Linear Algebra 74 Blas Jack Dongarra, Victor Eijkhout and Julien Langou .. Introduction 75 Lapack Bai, Demmel, Dongarra & Langou and Wang .. Introduction • Linear System of Equations • Linear Least Squares Problems • The Linear Equality-Constrained Least Squares Problem • A general Linear Model.

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### Subroutine package for processing large, sparse, least-squares problems by William H Dillinger Download PDF EPUB FB2

Get this from a library. Subroutine package for processing large, sparse, least-squares problems. [William H Dillinger; National Geodetic Survey (U.S.)].

Created Date: 5/19/ PM. Abstract. Numerical and computational aspects of direct methods for large and sparse least squares problems are considered. After a brief survey of the most often used methods, we summarize the important conclusions made from a numerical comparison in icantly improved algorithms have during the last 10–15 years made sparse QR factorization attractive, and competitive to Cited by: 6.

We consider solving the $\ell_1$-regularized least-squares ($\ell_1$-LS) problem in the context of sparse recovery for applications such as compressed sensing. The standard proximal gradient method, also known as iterative soft-thresholding when applied to this problem, has low computational cost per iteration but a rather slow convergence by: LSQR: Sparse Equations and Least Squares.

AUTHORS: Chris Paige, Michael Saunders. CONTRIBUTORS: James Howse, Michael Friedlander, John Tomlin, Miha Grcar, Jeffery Kline, Dominique Orban, Austin Benson, Victor Minden, Matthieu Gomez, Tim Holy.

CONTENTS: Implementation of a conjugate-gradient type method for solving sparse linear equations and sparse least-squares problems. This book describes, in a basic way, the most useful and effective iterative solvers and appropriate preconditioning techniques for some of the most important classes of large and sparse linear.

This is a library for solving large-scale nonlinear optimization problems. By employing sparse linear algebra, it is taylored for problems that sparse weak coupling between the optimization variables.

For appropriately sparse problems this results in massive performance gains. For smaller problems with dense Jacobians a dense mode is available also. Double Least Squares Pursuit for Sparse Decomposition of the least-squares approximation problem x up-to-date concepts in signal and least-squares problems book processing.

Written as a text-book for a graduate. SparseM: A Sparse Matrix Package for R Roger Koenker and Pin Ng March 7, To illustrate the functionality of the package we include an application to least squares regression.

The group of functions slm, sum- the feasibility of large problems and sparse storage is. 23nd Signal Processing and Communications SIRT- and CG-type methods for the iterative solution of sparse linear least-squares problems.

Linear Algebra and its A Chebyshev condition for accelerating convergence of iterative tomographic methods-solving large least squares problems. Physics of the Earth and Cited by: Many video processing algorithms are formulated as least-squares problems that result in large, sparse linear systems.

Solving such systems in real time is very demanding. This paper focuses on reducing the computational complexity of a direct Cholesky-decomposition-based solver.

Our ap-proximation scheme builds on the observation that, in well-Cited by: 7. Linear least squares: minimize [[ Ax - b [[ 2 () where A is a matrix with m rows and n columns, b is an m-vector, ~ is a scalar, and the given data A, b,), are real.

The matrix A will normally be large and sparse. It is deemed by means of a user-written subroutine APROD, whose. SparseM: A Sparse Matrix Package for R ∗ Roger Koenker and Pin Ng Decem Abstract SparseM provides some basic R functionality for linear algebra with sparse matrices.

Use of the package is illustrated by a family of linear model tting functions that implement least squares methods for problems with sparse design matrices. The main contribution of this thesis is the extension of tensor methods to large, sparse nonlinear equations and nonlinear least squares problems.

This involves an entirely new way of solving the tensor model that is efficient for sparse problems, and the consideration of a number of interesting linear algebraic implementation issues.

Dimension reduction techniques such as principal components analysis (PCA) or partial least squares (PLS) have recently gained much attention for addressing these within the context of genomic data (Boulesteix and Strimmer, ).Although dimension reduction via PCA or PLS is a principled way of dealing with ill-posed problems, it does not automatically lead to selection of relevant by: I'm looking for a software package to solve a very large, sparse non-linear least squares problem in C++.

I've come across a large number of modern linalg libraries in C++ (eigen, armadillo, boost, etc.), but none seem to have such a solver (or even a regular least-squares solver) built in.

Package ‘sparsesvd’ J Title Sparse Truncated Singular Value Decomposition (from 'SVDLIBC') Version Date Description Wrapper around the 'SVDLIBC' library for (truncated) singular value decomposi-tion of a sparse matrix. Currently, only sparse real matrices in Matrix package format are supported.

Depends R (>= ). to make Ax close to b. Least squares ﬁtting results when the 2-norm of Ax−b is used to quantify success. In § we introduce the least squares problem and solve a simple ﬁtting problem using built-in Matlab features.

In § we present the QR factorization and show how it can be used to solve the least squares Size: KB. The construction of this Estimation Subroutine Package (ESP) was motivated by an involvement with a particular problem; construction of fast, efficient and simple least squares data processing algorithms to be used for determining ephemeris corrections.

Discussion with. Duxbury led to the proposal of a subroutine strategy which would. What is the best function to obtain a least squares minimum solution from a linear problem like Ax = b in Octave, with A very large but sparse.

x = A\b gives the error: SparseQR: sparse matrix QR factorization filled" that I don't understand. Try a Faster Sparse Function. CHOLMOD includes a sparse2 mexFunction which is a replacement for sparse. It uses a linear-time bucket sort. The MATLAB (Rb) sparse accounts for about 3/4ths the total run time of wathen2.m.

For this matrix sparse2 in CHOLMOD is about 10 times faster than the MATLAB sparse. CHOLMOD can be found in the Author: Loren Shure. W. M. Gentleman, University of Waterloo, "Basic Description For Large, Sparse Or Weighted Linear Least Squares Problems (Algorithm AS 75)," Applied Statistics () Vol 23; No.

3. Gentleman's algorithm is the statistical standard. Insertion of a new observation can be done one observation at any time (WITH A WEIGHT!), and still only takes a.A Fortran IV subroutine to solve large sparse general systems of linear equations.

J.J. Dongarra, G.K. Leaf and M. Minkoff July, 1. Purpose The Fortran program ICCGLU solves a linear system of equations A*x = b, where A is a large sparse real gereral matrix.

The solution is found through an iterative procedure.