Lectures related to Catastrophic cancellation

Floating Point Representation in Computers

Covers the representation of real numbers in a computer using floating point representation and the dangers of significant digit cancellation.

Issues with STL; DFAM

Discusses known problems with .STL format, control parameters, issues with high aspect ratio parts, multimaterial parts, and introduces Design for Additive Manufacturing (DFAM) principles.

Floating Point Numbers: Representation and Errors

Explores floating point numbers, their representation, precision, and associated errors.

Floating Point Representation: Consequences for Programming

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

Numerical Derivatives of Order 1, Rounding Errors

Discusses numerical derivatives of order 1 and the effects of rounding errors on calculations.

Floating Point Numbers: LU Decomposition and Errors

Explores floating point numbers, LU decomposition, errors, and matrix properties.

Numerical Differentiation: Part 1

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

Numerical Derivatives: Finite Central Differences (2)

Explores the accuracy of central finite difference formulas for derivatives.

Information Representation: Computation Module

Explores the representation of information, rounding errors, and image encoding.

Floating Point Numbers: Representation and Errors

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

Nonlinear Equations: Representation of Real Numbers

Discusses the representation of real numbers in various bases and the implications of floating-point arithmetic.

Direct Methods for Solving Linear Equations

Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.

Numerical Differentiation

Discusses numerical differentiation, error analysis, and finite difference formulas.

Numerical Derivatives: Finite Difference Formulas

Analyzes the error in numerical derivatives using finite difference formulas.

Thomas algorithm, accuracy of direct methods

Explores the Thomas algorithm for tridiagonal systems and the accuracy of direct methods in numerical computations.

Polynomial Interpolation: Lagrange Method

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

Digital Systems: Fixed-Point and Floating-Point Arithmetic

Provides an overview of fixed-point and floating-point arithmetic in digital systems.

Numerical Methods in Matlab

Covers derivation, integration, and simulation in Matlab, along with the representation of numbers and potential errors.

Numerical Differentiation: Finite Differences

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

Floating Point Numbers: LU Decomposition and Errors

Explores floating point numbers, LU decomposition, errors in numerical computations, and the impact of round-off errors.