Lectures related to Approximation error

Covers numerical integration methods, focusing on trapezoidal rules, degree of exactness, and error analysis.

Explores the effect of rounding errors in solving linear systems using the LU factorization method.

Explores error analysis and limitations in interpolation on evenly distributed nodes.

Covers the stages of the explicit Runge-Kutta method for approximating y(t) with detailed explanations.

Explores numerical differentiation using finite differences and addresses the impact of errors in computer computations.

Explains spline interpolation and error analysis in approximating data points using piecewise linear and spline methods.

Explores iterative error calculation and the spectral radius significance in error analysis.

Covers advanced topics in numerical analysis, focusing on techniques for solving complex mathematical problems.

Covers the verification and validation process in numerical flow simulation, ensuring credibility of simulation outcomes.

Explores the representation of floating point numbers and the importance of error analysis.

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Discusses the binary representation of real numbers and the precision errors involved.

Covers the principles of quantum error correction, focusing on Shor's quantum error correction code.

Introduces floating point number representation, round-off errors, and their impact on numerical computations.

Summarizes the finite difference method for solving one-dimensional limit problems.

Explores the consequences of floating-point representation errors in programming, emphasizing precision and computational costs.

Covers the Lagrange polynomial interpolation method and error analysis in function approximation.

Explores finite differences formulas, error analysis, and numerical experiments in computational mathematics.

Analyzes the error in numerical derivatives using finite difference formulas.

Explores finite element interpolation using the Clément operator for non-continuous functions and discusses error estimation.