Modifying pivot elements in Gaussian elimination
نویسندگان
چکیده
منابع مشابه
Modifying pivot elements in Gaussian elimination
The rounding-error analysis of Gaussian elimination shows that the method is stable only when the elements of the matrix do not grow excessively in the course of the reduction. Usually such growth is prevented by interchanging rows and columns of the matrix so that the pivot element is acceptably large. In this paper the alternative of simply altering the pivot element is examined. The alterati...
متن کاملGaussian elimination
As the standard method for solving systems of linear equations, Gaussian elimination (GE) is one of the most important and ubiquitous numerical algorithms. However, its successful use relies on understanding its numerical stability properties and how to organize its computations for efficient execution on modern computers. We give an overview of GE, ranging from theory to computation. We explai...
متن کاملHow Ordinary Elimination Became Gaussian Elimination
Newton, in an unauthorized textbook, described a process for solving simultaneous equations that later authors applied specifically to linear equations. This method — that Newton did not want to publish, that Euler did not recommend, that Legendre called “ordinary,” and that Gauss called “common” — is now named after Gauss: “Gaussian” elimination. (One suspects, he would not be amused.) Gauss’s...
متن کاملSparse Gaussian Elimination Andorthogonal
We consider the solution of a linear system Ax = b on a distributed memory machine when the matrix A has full rank and is large, sparse and nonsymmetric. We use our Cartesian nested dissection algorithm to compute a ll-reducingcolumn ordering of the matrix. We develop algorithms that use the associated separator tree to estimate the structure of the factor and to distribute and perform numeric ...
متن کاملGaussian elimination without rounding
The usual procedure to compute the determinant is the so-called Gaussian elimination. We can view this as the transformation of the matrix into a lower triangular matrix with column operations. These transformations do not change the determinant but in the triangular matrix, the computation of the determinant is more convenient: we must only multiply the diagonal elements to obtain it. (It is a...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1974
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1974-0343559-8