COL726: Difference between revisions
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| credits = 4 | | credits = 4 | ||
| credit_structure = 3-0-2 | | credit_structure = 3-0-2 | ||
| pre_requisites = MTL106 | | pre_requisites = [[MTL106]] | ||
| overlaps = MTL704 | | overlaps = [[MTL704]] | ||
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== COL726 : Numerical Algorithms == | == COL726 : Numerical Algorithms == | ||
Number representation, fundamentals of error analysis, conditioning, stability, polynomials and root finding, interpolation, singular value decomposition and its applications, QR factorization, condition number, least squares and regression, Gaussian elimination, eigenvalue computations and applications, iterative methods, linear programming, elements of convex optimization including steepest descent, conjugate gradient, Newton's method. COL727 Rapid Mixing in Markov Chains Credits: 3 (3-0-0) Basic of finite Markov chains; classical Markov Chains including Coupon collection, Gambler's Ruin, Polya's um, Birth and Death chains; Total Variation Distance; the Convergence Theorem; Mixing Time; bounding mixing time via couplings; bounding mixing time via strong stationary times; random walks on networks; bounding mixing time via hitting times; cover times; spectral bounds on mixing time; mixing time bounds via comparison between chains. | Number representation, fundamentals of error analysis, conditioning, stability, polynomials and root finding, interpolation, singular value decomposition and its applications, QR factorization, condition number, least squares and regression, Gaussian elimination, eigenvalue computations and applications, iterative methods, linear programming, elements of convex optimization including steepest descent, conjugate gradient, Newton's method. [[COL727]] Rapid Mixing in Markov Chains Credits: 3 (3-0-0) Basic of finite Markov chains; classical Markov Chains including Coupon collection, Gambler's Ruin, Polya's um, Birth and Death chains; Total Variation Distance; the Convergence Theorem; Mixing Time; bounding mixing time via couplings; bounding mixing time via strong stationary times; random walks on networks; bounding mixing time via hitting times; cover times; spectral bounds on mixing time; mixing time bounds via comparison between chains. | ||
Latest revision as of 16:26, 14 April 2026
| COL726 | |
|---|---|
| Numerical Algorithms | |
| Credits | 4 |
| Structure | 3-0-2 |
| Pre-requisites | MTL106 |
| Overlaps | MTL704 |
COL726 : Numerical Algorithms
Number representation, fundamentals of error analysis, conditioning, stability, polynomials and root finding, interpolation, singular value decomposition and its applications, QR factorization, condition number, least squares and regression, Gaussian elimination, eigenvalue computations and applications, iterative methods, linear programming, elements of convex optimization including steepest descent, conjugate gradient, Newton's method. COL727 Rapid Mixing in Markov Chains Credits: 3 (3-0-0) Basic of finite Markov chains; classical Markov Chains including Coupon collection, Gambler's Ruin, Polya's um, Birth and Death chains; Total Variation Distance; the Convergence Theorem; Mixing Time; bounding mixing time via couplings; bounding mixing time via strong stationary times; random walks on networks; bounding mixing time via hitting times; cover times; spectral bounds on mixing time; mixing time bounds via comparison between chains.