Author | Ueberhuber, Christoph W. author |
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Title | Numerical Computation 1 [electronic resource] : Methods, Software, and Analysis / by Christoph W. Ueberhuber |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1997 |
Connect to | http://dx.doi.org/10.1007/978-3-642-59118-1 |
Descript | XVI, 474 p. 31 illus. online resource |
1 Scientific Modeling -- 1.1 Reality Versus Model -- 1.2 The Model Subject and the Model -- 1.3 The Model Subject and Reality -- 1.4 Model Building -- 2 Fundamental Principles of Numerical Methods -- 2.1 From Application Problems to their Numerical Solution -- 2.2 Numerical Problems -- 2.3 Types of Errors in Numerics -- 2.4 The Condition of Mathematical Problems -- 2.5 The Condition of Application Problems -- 2.6 The Mathematical Elements of Condition Estimation -- 2.7 Validation of Numerical Computations -- 3 Computers for Numerical Data Processing -- 3.1 Processors -- 3.2 Memory -- 3.3 Performance Quantification -- 3.4 Analytical Performance Assessment -- 3.5 Empirical Performance Assessment -- 4 Numerical Data and Numerical Operations -- 4.1 Mathematical Data -- 4.2 Numerical Data on Computers -- 4.3 Operations on Numerical Data -- 4.4 Number Systems on Computers -- 4.5 Structure of Floating-Point Systems -- 4.6 Standardization of Floating-Point Number Systems -- 4.7 Arithmetics for Floating-Point Systems -- 4.8 Inquiry Functions and Manipulation of Numbers in Fortran 90 -- 4.9 Operations with Algebraic Data -- 4.10 Operations with Arrays -- 4.11 Operations with Analytic Data -- 5 Numerical Algorithms -- 5.1 The Intuitive Notion of an Algorithm -- 5.2 Properties of Algorithms -- 5.3 Existence of Algorithms -- 5.4 Practical Solvability of Problems -- 5.5 Complexity of Algorithms -- 5.6 Representation of Algorithms -- 5.7 Influence of Rounding Errors on Numerical Algorithms -- 5.8 Case Study: Floating-Point Summation -- 6 Numerical Programs -- 6.1 The Quality of Numerical Programs -- 6.2 Reasons for Poor Efficiency -- 6.3 The Measurement of Performance Indices -- 6.4 Performance Optimization -- 6.5 Architecture Independent Optimizations -- 6.6 Loop Optimizations -- 6.7 Blocked Memory Access -- 6.8 Case Study: Multiplication of Matrices -- 7 Available Numerical Software -- 7.1 The Cost of Software -- 7.2 Sources of Numerical Software -- 7.3 Software and the Internet -- 7.4 Interactive Multifunctional Systems -- 7.5 Problem Solving Environments -- 7.6 Case Study: Software for Elliptic PDEs -- 8 Using Approximation in Mathematical Model Building -- 8.1 Analytic Models -- 8.2 Information and Data -- 8.3 Discrete Approximation -- 8.4 Function Approximation -- 8.5 Choosing a Model Function -- 8.6 Choice of the Distance Function -- 8.7 Transformation of the Problem -- 9 Interpolation -- 9.1 Interpolation Problems -- 9.2 Mathematical Foundations -- 9.3 Univariate Polynomial Interpolation -- 9.4 Univariate, Piecewise, Polynomial Interpolation -- 9.5 Polynomial Splines -- 9.6 B-Splines -- 9.7 Cubic Spline Interpolation -- 9.8 Splines Without Undesirable Oscillations -- 9.9 Multivariate Interpolation -- 9.10 Multivariate Polynomial Interpolation -- 9.11 Multivariate (Sub-) Spline Interpolation -- 9.12 Related Problems and Methods -- Glossary of Notation -- Author Index