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Curve Fitting, Precision Interpolation, and Function Approximation |
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– 1st and 2nd derivative methods
– Bilinear Interpolation
– Cubic and Bi-Cubic Splines
– ejwt Precision Time Shift
– Hunting Behavior Considerations
– Multi-dimensional methods
– Polynomial and Parabolic Interpolation
– Regression Techniques
– Sinc Squared
– Steins Method
– Volterra Series
– Weighted Least Squares
– Zero-Pad FFT/IFFT methods
– Additional related procedures |
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Root Finding, Linear and Nonlinear Systems |
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– Bracketing, Bisection
– Brent's Method
– Eigenvalue Decomposition
– Gaussian Elimination and Backsubstitution
– LU Decomposition
– Piecewise Linear methods
– Polynomial Roots
– Secant, Newton-Raphsen methods, Derivatives and "Root Polishing"
– Additional Root Finding methods |
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Automated Graphics and Scientific Visualization |
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– "Movies" to show time-varying behavior of simulated systems
– Generation of Color Reports and Presentations
– Proof of Concept visualizations
– System-level design of graphic display formats
– Various 2-D, 3-D, and 4-D (pseudocolor) methods of data portrayal
– Additional Visualization techniques
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Data Modeling and Statistical Description |
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– Central Limit Theorem
– Chi-Square techniques
– Cramer-Rao accuracy limitations
– Cumulative & Gaussian Distributions
– Efficient Median Search
– Histograms
– Kalman Filtering
– Linear and Nonlinear Models
– Mean, Variance, Skewness
– Optimal Data Smoothing
– Probability Density
– Statistical and Systematic Error Analysis
– Other Data Measurement, Classification and Modeling techniques |
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Minimization/Optimization of Functions |
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– Global vs. Local Minima
– Gradients and Hessian Matrices
– Multi-dimensional Nelder-Meade Simplex
– Powell's Method
– Steepest Descent, Conjugate Gradient
– Additional related processes |
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Computers, Errors, and Algorithms |
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– Accuracy and Precision Improvement
– Quantization and Roundoff Error handling
– Random and Pseudo-Random Numbers
– Managing other Hardware Idiosyncrasies |
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Other Numerical Methods |
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– Acceleration of Convergence
– Closed Form Solutions
– Continuous Functions
– Finite Differences in Derivative Formulas and Differential Equations.
– Monte-Carlo Methods
– Numerical Integration and Differentiation
– Runge-Kutta methods
– Various other Numerical Methods and allied DSP methods (see previous area)
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