Roundoff-Error-Free Algorithms for Solving Linear Systems via Cholesky and LU Factorizations

نویسندگان

  • Adolfo R. Escobedo
  • Erick Moreno-Centeno
چکیده

Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title. However, use of a template does not certify that the paper has been accepted for publication in the named journal. INFORMS journal templates are for the exclusive purpose of submitting to an INFORMS journal and should not be used to distribute the papers in print or online or to submit the papers to another publication.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

WZ factorization via Abay-Broyden-Spedicato algorithms

Classes of‎ ‎Abaffy-Broyden-Spedicato (ABS) methods have been introduced for‎ ‎solving linear systems of equations‎. ‎The algorithms are powerful methods for developing matrix‎ ‎factorizations and many fundamental numerical linear algebra processes‎. ‎Here‎, ‎we show how to apply the ABS algorithms to devise algorithms to compute the WZ and ZW‎ ‎factorizations of a nonsingular matrix as well as...

متن کامل

Improved Backward Error Bounds for LU and Cholesky Factorizations

Assuming standard floating-point arithmetic (in base β, precision p) and barring underflow and overflow, classical rounding error analysis of the LU or Cholesky factorization of an n×n matrix A provides backward error bounds of the form |∆A| 6 γn|L̂||Û | or |∆A| 6 γn+1|R̂ ||R̂|. Here, L̂, Û , and R̂ denote the computed factors, and γn is the usual fraction nu/(1−nu) = nu+O(u2) with u the unit roundo...

متن کامل

Review of Matrix Decomposition Techniques for Signal Processing Applications

Decomposition of matrix is a vital part of many scientific and engineering applications. It is a technique that breaks down a square numeric matrix into two different square matrices and is a basis for efficiently solving a system of equations, which in turn is the basis for inverting a matrix. An inverting matrix is a part of many important algorithms. Matrix factorizations have wide applicati...

متن کامل

Communication-optimal Parallel and Sequential Cholesky Decomposition

Numerical algorithms have two kinds of costs: arithmetic and communication, by which we mean either moving data between levels of a memory hierarchy (in the sequential case) or over a network connecting processors (in the parallel case). Communication costs often dominate arithmetic costs, so it is of interest to design algorithms minimizing communication. In this paper we first extend known lo...

متن کامل

Algebraic Algorithms

This is a preliminary version of a Chapter on Algebraic Algorithms in the upcoming Computing Handbook Set Computer Science (Volume I), CRCPress/Taylor and Francis Group. Algebraic algorithms deal with numbers, vectors, matrices, polynomials, formal power series, exponential and differential polynomials, rational functions, algebraic sets, curves and surfaces. In this vast area, manipulation wit...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • INFORMS Journal on Computing

دوره 27  شماره 

صفحات  -

تاریخ انتشار 2015