Numerical Matrix Analysis - Linear Systems and Least Squares
نویسنده
چکیده
Or use your credit card (AMEX, MasterCard, and VISA): Call SIAM Customer Service at +1-215-382-9800 worldwide · Fax: +1-215-386-7999 E-mail: [email protected]. Send check or money order in US dollars to: SIAM, Dept. BKIL09, 3600 Market Street, 6th Floor, Philadelphia, PA 19104-2688 USA. Members and customers outside North America can also order SIAM books through Cambridge University Press at www.cambridge.org/siam. Numerical Matrix Analysis: Linear Systems and Least Squares Ilse C. F. Ipsen This self-contained textbook presents matrix analysis in the context of numerical computation with numerical conditioning of problems and numerical stability of algorithms at the forefront. Using a unique combination of numerical insight and mathematical rigor, it advances readers’ understanding of two phenomena: sensitivity of linear systems and least squares problems, and numerical stability of algorithms. The material is presented at a basic level, emphasizing ideas and intuition, and each chapter offers simple exercises for use in the classroom and more challenging exercises for student practice.
منابع مشابه
Positive solution of non-square fully Fuzzy linear system of equation in general form using least square method
In this paper, we propose the least-squares method for computing the positive solution of a $mtimes n$ fully fuzzy linear system (FFLS) of equations, where $m > n$, based on Kaffman's arithmetic operations on fuzzy numbers that introduced in [18]. First, we consider all elements of coefficient matrix are non-negative or non-positive. Also, we obtain 1-cut of the fuzzy number vector solution of ...
متن کاملNEW MODELS AND ALGORITHMS FOR SOLUTIONS OF SINGLE-SIGNED FULLY FUZZY LR LINEAR SYSTEMS
We present a model and propose an approach to compute an approximate solution of Fully Fuzzy Linear System $(FFLS)$ of equations in which all the components of the coefficient matrix are either nonnegative or nonpositive. First, in discussing an $FFLS$ with a nonnegative coefficient matrix, we consider an equivalent $FFLS$ by using an appropriate permutation to simplify fuzzy multiplications. T...
متن کاملGlobal least squares solution of matrix equation $sum_{j=1}^s A_jX_jB_j = E$
In this paper, an iterative method is proposed for solving matrix equation $sum_{j=1}^s A_jX_jB_j = E$. This method is based on the global least squares (GL-LSQR) method for solving the linear system of equations with the multiple right hand sides. For applying the GL-LSQR algorithm to solve the above matrix equation, a new linear operator, its adjoint and a new inner product are dened. It is p...
متن کاملUsing an Efficient Penalty Method for Solving Linear Least Square Problem with Nonlinear Constraints
In this paper, we use a penalty method for solving the linear least squares problem with nonlinear constraints. In each iteration of penalty methods for solving the problem, the calculation of projected Hessian matrix is required. Given that the objective function is linear least squares, projected Hessian matrix of the penalty function consists of two parts that the exact amount of a part of i...
متن کاملTikhonov Regularization and Total Least Squares
Discretizations of inverse problems lead to systems of linear equations with a highly ill-conditioned coefficient matrix, and in order to compute stable solutions to these systems it is necessary to apply regularization methods. We show how Tikhonov’s regularization method, which in its original formulation involves a least squares problem, can be recast in a total least squares formulation sui...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009