Concept
Approximation error
Related lectures (120)
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Covers the representation of real numbers in a computer using floating point representation and the dangers of significant digit cancellation.
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Delves into troubleshooting errors and pitfalls in electronic structure methods, emphasizing the importance of integration grids and functional choices.
Conservation of Energy in Newmark Scheme
Explores the conservation of energy in the Newmark scheme and its implications for stability and error estimates.
Composite Formulas Analysis
Discusses the analysis of composite numerical integration formulas and their convergence, stability, and error characteristics.
Numerical Integration: Trapezoidal Rule
Covers numerical integration methods, focusing on the trapezoidal rule and iterative processes.
Numerical Integration: Simpson Quadrature Rule
Covers the Simpson quadrature rule for numerical integration, explaining the method to compute integrals using interpolation nodes and weights.
Numerical Differentiation: Backward and Central Differences
Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.
Direct Methods for Solving Linear Equations
Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.
Norm Equivalence and Inverse Inequality
Explores norm equivalence, inverse inequality, and error analysis in finite element methods.