Introduction to Numerical ComputationAnalysis and Matlab illustrations

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Introduction to Numerical ComputationAnalysis and Matlab illustrations

Introduction to Numerical ComputationAnalysis and Matlab illustrations

This ebook contains the following
topics: Mathematical Models and Numerical Approximations, Numerical Computation,
References, Sources of Error, Basic Concepts, Error Propagation, Number
Representation, Rounding Errors in Floating Point, Arithmetic Operations in
Floating Point, Accumulated Errors, IEEE Standard, Introduction, Remainder Term
Estimates, Standard Functions, Range Reduction, Trigonometric Functions,
Introduction, Crude Localization, Iteration Methods, Convergence Analysis, Error
Estimation and StoppingCriteria, Algebraic Equations, Square Root, Nonlinear
Systems, Introduction, Interpolation by Polynomials, Linear Interpolation,
Lagrange Interpolation, Hermite Interpolation, Splines, Linear Spline Functions,
Cubic Splines, Introduction, Richardson Extrapolation, Introduction, Trapezoidal
Rule, Adaptive Quadrature, Introduction, Triangular Systems, Gaussian
Elimination, Pivoting, LU Factorization, Band Matrices, Inverse Matrix, Vector
and Matrix Norms, Sensitivity Analysis, Rounding Errors, Estimation of Condition
Number, Overdetermined Systems, QR Factorization, Introduction, Important
Concepts, Least Squares Method, Orthogonal Functions, Orthogonal Polynomials,
Legendre Polynomials, Chebyshev Polynomials, Discrete Cosine Transform, Minimax
Approximation, Introduction, Initial Value Problems, Local and Global Error, An
Implicit Method, Stability, Adaptive Step Length Control, Boundary Value
Problems, A Finite Element Method, The Shooting Method, Mathematical Models and
Numerical Approximations

Author(s): Lars Elden
Linde Wittmeyer-Koch Hans Bruun Nielsen

This ebook contains the following
topics: Mathematical Models and Numerical Approximations, Numerical Computation,
References, Sources of Error, Basic Concepts, Error Propagation, Number
Representation, Rounding Errors in Floating Point, Arithmetic Operations in
Floating Point, Accumulated Errors, IEEE Standard, Introduction, Remainder Term
Estimates, Standard Functions, Range Reduction, Trigonometric Functions,
Introduction, Crude Localization, Iteration Methods, Convergence Analysis, Error
Estimation and StoppingCriteria, Algebraic Equations, Square Root, Nonlinear
Systems, Introduction, Interpolation by Polynomials, Linear Interpolation,
Lagrange Interpolation, Hermite Interpolation, Splines, Linear Spline Functions,
Cubic Splines, Introduction, Richardson Extrapolation, Introduction, Trapezoidal
Rule, Adaptive Quadrature, Introduction, Triangular Systems, Gaussian
Elimination, Pivoting, LU Factorization, Band Matrices, Inverse Matrix, Vector
and Matrix Norms, Sensitivity Analysis, Rounding Errors, Estimation of Condition
Number, Overdetermined Systems, QR Factorization, Introduction, Important
Concepts, Least Squares Method, Orthogonal Functions, Orthogonal Polynomials,
Legendre Polynomials, Chebyshev Polynomials, Discrete Cosine Transform, Minimax
Approximation, Introduction, Initial Value Problems, Local and Global Error, An
Implicit Method, Stability, Adaptive Step Length Control, Boundary Value
Problems, A Finite Element Method, The Shooting Method, Mathematical Models and
Numerical Approximations

Author(s): Lars Elden
Linde Wittmeyer-Koch Hans Bruun Nielsen

This note explains the following topics: Numerical linear
algebra, nonlinear optimization, nonlinear least squares, introduction to
floating point numbers and rounding error, examples from signal and image
processing, control, machine learning.

This
note explains the following topics: computing with Matrices and Vectors, Direct
Methods for Linear Systems of Equations, DIrect Methods for Linear Least Squares
Problems, Filtering Algorithms, Data Interpolation and Data Fitting in 1D,
Approximation of Functions in 1D , Numerical Quadrature, Iterative Methods for
Non-Linear Systems of Equations, Eigenvalues, Numerical Integration, Structure
Preserving Integration.

This manual describes the
floating-point environment supported by software and hardware on SPARCTM and x86
platforms running the Solaris operating system.

This book
covers the following topics: Computers for which LAPACK is Suitable, LAPACK Compared with LINPACK and EISPACK, LAPACK and the BLAS, Availability of LAPACK, Commercial Use of LAPACK, Installation of LAPACK, Documentation for LAPACK, Support for LAPACK
and
Errata in LAPACK.

Author(s): E.
Anderson , Z. Bai , C. Bischof , L. S. Blackford , J. Demmel , J. Dongarra , J.
Du Croz , A. Greenbaum , S. Hammarling , A. McKenney and D. Sorensen