Lecture

Linear Algebra: Efficiency and Complexity

Related lectures (29)

Covers optimization algorithms, convergence properties, and time complexity of sequences and functions.

Covers Dijkstra's algorithm and its application to the all-pairs shortest path problem.

Explores linear programming optimization with constraints, Dijkstra's algorithm, and LP formulations for finding feasible solutions.

Explores practical aspects of solving parity games, including winning strategies, algorithms, complexity, determinism, and heuristic approaches.

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Introduces an improved algorithm for three-color parity games, focusing on progress measures, acceleration, and practical speed-up.

Explores convex polyhedra, linear programs, and their optimization importance.

Covers the basics of linear programming, defining corners, extreme points, and feasible solutions within polyhedrons.

Covers worst-case complexity, algorithms, and proofs including mathematical induction and recursion.

Explores orthogonal projections, symmetry of matrices, and their applications.

Covers coin rendering and the limitations of the greedy algorithm in finding optimal solutions.

Compares random and symmetrical graph coloring in terms of cluster colorability and equilibrium.

Covers algorithmic complexity and travel time analysis, focusing on measuring the time taken by algorithms and evaluating their performance.

Explores extreme points in linear programming and the role of constraints in finding optimal solutions.

Focuses on open problems and the importance of reformulating problems with better tools and intuition.

Explores the complexity of linear algebra operations and optimization methods, including Gaussian elimination and the simplex method.

Explores algorithm complexity, analyzing efficiency and worst-case scenarios of sorting algorithms.

Explores dynamic programming through Pascal's Triangle and Floyd's Algorithm.

Explores algorithmic complexity, comparing growth rates using Theta notation and characterizing different complexity classes.

Covers the concept of convex functions and their applications in optimization problems.