2 edition of **solution of the general least squares problem with special reference to high-speed computers** found in the catalog.

solution of the general least squares problem with special reference to high-speed computers

University of California. Los Alamos Scientific Laboratory.

- 60 Want to read
- 37 Currently reading

Published
**1960**
in Washington
.

Written in English

**Edition Notes**

Statement | by R.H. Moore, R.K. Zeigler. |

Series | Report LA-2367 |

Contributions | Moore, R H., Zeigler, R K. |

ID Numbers | |
---|---|

Open Library | OL20750933M |

Numerical Solution of Differential Equations7. Least-Squares Polynomial ApproximationIn this revised and updated second edition, Professor Hildebrand (Emeritus, Mathematics, MIT) made a special effort to include more recent significant developments in the field, increasing the focus on concepts and procedures associated with computers. The U.S. Department of Energy's Office of Scientific and Technical Information.

by Least Squares," in Technometrics, Vol. 3, No. 2, May , pp. _I The following manuals, which include a computer program, would I also be extremely useful in finding the above estimates: I 1! I "The Solution of the General Least Squares Problem with Special Reference to High-speed Computers" LA and LA addenda. Examples of Statistical Learning problems include: ordinary least squares is the major criteria to be considered to fit them into the data. A spline is a special function defined piecewise.

ISBN: OCLC Number: Description: xvii, pages: illustrations ; 26 cm: Contents: Mathematical and statistical properties of least squares solutions --Basic numerical methods --Modified least squares problems --Generalized least squares problems --Constrained least squares problems --Direct methods for sparse problems --Iterative methods for least squares. Numerical analysis, area of mathematics and computer science that creates, analyzes, and implements algorithms for obtaining numerical solutions to problems involving continuous variables. Such problems arise throughout the natural sciences, social sciences, engineering, medicine, and business. Since the mid 20th century, the growth in power and availability of digital computers has led to an.

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@article{osti_, title = {THE SOLUTION OF THE GENERAL LEAST SQUARES PROBLEM WITH SPECIAL REFERENCE TO HIGH-SPEED COMPUTERS}, author = {Moore, R H and Zeigler, R K}, abstractNote = {The general problem of least squares analysis is discussed.

Special emphasis is placed on functions in which the parameters appear nonlinearly and which can be fitted by Gauss'. THE SOLUTION OF THE GENERAL LEAST SQUARES PROBLEM WITH SPECIAL REFERENCE TO HIGH-SPEED COMPUTERS.

By P. McWilliams. Cite. BibTex; Full citation; Abstract. This report extends and revises LA Changes in the Los Alamos non- linear least squares program are outlined. A condensed guide for the data card arrangement is presented.

Author: P. McWilliams. The solution of the general least squares problem with special reference to high-speed computers / By R. (Raymond H.) Moore, R. Zeigler, U.S. Atomic Energy Commission. and Los Alamos Scientific Laboratory. Solution of Rank Deﬁcient Least Squares Problems If rank(A) problem), then inﬁnitely many solutions exist.

A common approach to obtain a well-deﬁned solution in this case is to add an additional constraint of the form kxk −→ min,File Size: KB. Answer to Compute the least-squares error associated with the least-squares solution x of Ax b.

1 -2 1 74 10 -1 2 A- b- 0 45 2. Moore and R. Ziegler, “The Solution of the General Least Squares Problem with Special Reference to High‐Speed Computers,” U.S. Department of Commerce, Bull. LA, March Google Scholar; Details on computer programs are available from K.

J., Department of Chemistry, University of Pittsburgh, Pittsburgh, Pa., 2 Chapter 5. Least Squares The symbol ≈ stands for “is approximately equal to.” We are more precise about this in the next section, but our emphasis is on least squares approximation. The basis functions ϕj(t) can be nonlinear functions of t, but the unknown parameters, βj, appear in the model system of linear equations.

LECTURE GENERALIZED LEAST SQUARES (GLS) In this lecture, we will consider the model y = Xβ+ εretaining the assumption Ey = Xβ. However, we no longer have the assumption V(y) = V(ε) = σ2I. Instead we add the assumption V(y) = V where V is positive definite. Sometimes we take V = σ2Ωwith tr Ω= N As we know, = (X′X)-1X′y.

What is E. Least-squares (approximate) solution • assume A is full rank, skinny • to ﬁnd xls, we’ll minimize norm of residual squared, krk2 = xTATAx−2yTAx+yTy • set gradient w.r.t. x to zero: ∇xkrk2 = 2ATAx−2ATy = 0 • yields the normal equations: ATAx = ATy • assumptions imply ATA invertible, so we have xls = (ATA)−1ATy a very famous formula.

The general least-squares problem is to find an [x] that makes A[x] as close as possible to [b]. T A least-squares solution of A[x] = [b] is a vector x-hat that satisfies A(x-hat) = b-hat, where b-hat is the orthogonal projection of [b] onto ColA.

Moore and R. Zeigler, "The solution of gen eral least squares problem with special reference to high-speed computers, " Techn. Rep. LA, Univ. of California, Los Alamos (). solutions, and all of them are correct solutions to the least squares problem. (In general, if a matrix C is singular then the system Cx = y may not have any solution.

However, due to the structure of the least squares problem, in our case A0A will always have a solution, even if it is singular.). Solution of a least squares problem if A has linearly independent columns (is left-invertible), then the vector xˆ = „ATA” 1ATb = Ayb is the unique solution of the least squares problem minimize kAx bk2 in other words, if x, xˆ, then kAx bk2 > kAxˆ bk2 recall from page that Ay = „ATA” 1AT is called the pseudo-inverse of a left-invertible matrix.

R.H. MOORE and R. ZIEGLER, "The Solution of the General Least Squares Problems with Special Reference to High-Speed Computers" Los Alamos Scientific Laboratory Report LA (March ). The computer program has subsequently been updated.

R.G. DENNING, T. SNELLGROVE, and D. WOODWARK, Mol. Phys (). QR_SOLVE, a C++ library which computes a linear least squares (LLS) solution of a system A*x=b. There are many possible cases that can arise with the matrix A. Formally, we distinguish the cases M N, and we expect trouble whenever M is not equal to N.

Trouble may also arise when M = N but the matrix is singular. Reference: In Exercises 1–4, find a least-squares solution of A x = b by (a) constructing the normal equations for and (b) solving for Step-by-step solution.

The reader of this book should be familiar with the material in an elementary graduate level course in numerical analysis, in particular direct and iterative methods for the solution of linear equations and linear least squares problems. The material in texts such as [] and [] is sufﬁcient.

As a result, he developed a book that in the early chapters provides the linear algebra necessary for a study of how to perform accurate computation in such problems such as solving general and specialized square linear systems, least-squares, computation of eigenvalues, and the iterative solution.

1 Description of the Problem 1 2 Probability and Statistics Review 2 3 The Method of Least Squares 4 1 Description of the Problem Often in the real world one expects to ﬁnd linear relationships between variables.

For example, the force of a spring linearly depends on the displacement of. The Book should roughly include these topics: linear least squares regression; variance, covariance. regression coefficient. coefficient of determination. residual analysis (esp.

MathJax reference. To learn more, see our tips on writing great answers. Sign up or log in. Sign up using Google Least Squares solution for a symmetric singular matrix. Hot Network Questions In Dune, how do people cope with the lack of computers?The chemical shifts and linewidths of a series of 18 liquid inorganic chlorides have been measured using 35Cl broadline NMR techniques.

The chemical shifts vary from – ppm downfield from the chloride ion. Assuming the mean excitation energies of these compounds are equal, a rough correlation of shift with quadrupole coupling constants is obtained for the nontransitional metal chlorides.

() A two-dimensional Riemann solver with self-similar sub-structure – Alternative formulation based on least squares projection. Journal of Computational Physics() A characteristic space–time conservation element and solution element method for conservation laws II.