Lectures related to Floating Point Numbers: LU Decomposition and Errors

Floating Point Numbers: LU Decomposition and Errors

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

Thomas algorithm, accuracy of direct methods

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

Effect of Rounding Errors in Linear Systems

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

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.

Cholesky Factorization: Theory and Algorithm

Explores the Cholesky factorization method for symmetric positive definite matrices.

Floating Point Numbers: Representation and Errors

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

Numerical Methods in Matlab

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

Direct Methods for Linear Systems of Equations

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

Digital Systems: Fixed-Point and Floating-Point Arithmetic

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

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

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.

Number Systems: Fixed and Floating-Point Representations

Discusses fixed-point and floating-point representations in digital systems, covering key concepts like precision, accuracy, and the IEEE 754 standard.

Digital Systems: Fixed and Floating Point Arithmetic

Discusses fixed-point and floating-point arithmetic in digital systems, covering operations, representations, and the implications of rounding errors.

Numerical Differentiation: Part 1

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

Floating Point Representation: Consequences for Programming

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

Computer Arithmetic: Floating Point Numbers

Explores computer arithmetic, emphasizing fixed-point and floating-point numbers, IEEE 754 standard, dynamic range, and floating-point operations in MIPS architecture.

Number Systems: Fixed and Floating-Point Representations

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

Sensitivity of Solutions

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Direct Methods for Solving Linear Equations

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