Numerical Methods using MATLAB

✍ Scribed by Gupta, Abhishek

• Publisher: Apress
• Year: 2015
• Tongue: English
• Leaves: 147
• Series: EBL-Schweitzer
• Edition: Online-ausg
• Category: Library

✦ Synopsis

Matrix OperationsDot (array) Operators; Arithmetic Operators; Logical Operators; Relational Operators; Operations for Models; Indexing; Normal Indexing; Linear Indexing; Logical Indexing; Clipping a Signal; Halving a Matrix; Vectorization; Example 1. Creating C such that C(i, j)=A(i)^B(j); Example 2. Calculating the Sum of Harmonics; Example 3. Conversion to Matrix Operations; Example 4. Selective Inversion; Tips for Performance Improvement; Vectorization; First Attempt: Two Loops; Second Attempt: One Loop; Third Attempt: No Loop; Preallocating Arrays; Fixed Type Variables.

Chapter 3: Numerical TechniquesDifferentiation; Partial Differentiation; Computing Higher Derivatives; Integration; Multi-dimensional Integration; Integration Over an Infinite Range; Multidimensional Integration over Non-rectangular Intervals; Solving Equations; Polynomial Functions; Zeros of a General Function; Interpolation; One-dimensional Interpolation; Nearest Neighbor Interpolation; Linear Interpolation; Cubic Spline Interpolation; Cubic Interpolation; Spline Interpolation; Data Fitting and Polynomial Interpolation; Arbitrary Interpolation; Chapter 4: Visualization; Line Plots.

Plot OptionsMultiple Plots; Annotations; Handles; 2D plots; Quiver Plots; 3D Plots; Animations; A Clock Animation; Wave Motion; Movies; Chapter 5: Introduction to Simulation; One Step Simulations; Iterative Methods; Simulation of Real World Processes; Discrete Processes; Random Walks; Animation of the walk; Adding Drift; Simulation of Continuous Time Processes; Example: Balls in a 2D Box; Animation; Motion in a Force Field; Event-based Simulations; Chapter 6: Monte Carlo Simulations; Random Sampling; The Third Moment of a Gaussian Random Variable; Moments of Random Processes.

Sampling Realizations of the ProcessTime Averaging; Time Sampling; Sampling from a Given Distribution; Inbuilt Functions; Uniform Distribution; Gaussian Distribution; Exponential Distribution; Bernoulli Distribution; Rejection Sampling; Gibbs Sampling; Statistical Performance; Computation of pi; Communication Channels; Birth-Death Processes; Multidimensional Integrals; Summary; Chapter 7: Optimization; Optimization Overview; The Optimization Goal; Design Parameters; Constraints; The Optimization Domain; The Optimization Problem; Mathematical Approach; Implementation; Extensive Search.

The Gradient Descent Method.

Numerical Methods with MATLAB provides a highly-practical reference work to assist anyone working with numerical methods. A wide range of techniques are introduced, their merits discussed and fully working MATLAB code samples supplied to demonstrate how they can be coded and applied. Numerical methods have wide applicability across many scientific, mathematical, and engineering disciplines and are most often employed in situations where working out an exact answer to the problem by another method is impractical. Numerical Methods with MATLAB presents each topic in a concise and readable.

✦ Subjects

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