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algorithm%20topics

# algorithm%20topics - • Secant method o Two initial...

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COMP 208 Topics on Algorithms Searching Finding maximum and minimum – O(n) Linear search – O(n) Binary search for sorted data – O(log n) Sorting Bubble sort – O(n 2 ) o Optimized version Selection sort – O(n 2 ) Insertion sort – O(n 2 ) Recursive versions vs non-recursive versions Merging sorted lists – O(n) Mergesort -- O(n log n) Linear Algebra Vector operations o Addition, scaling, dot product, norm Matrix representation and operations o Add, transpose o Multiply – O(n 3 ) Solving linear systems o Gausian elimination without pivoting o Gaussian elimination with partial pivoting o Backsubstitution Root Finding Bisection algorithm o Two initial approximations that bracket a root o Guaranteed but slow convergence

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Unformatted text preview: • Secant method o Two initial approximations, not necessarily bracketing a root o Not guaranteed to converge but faster • False Position method o Two initial approximations that bracket a root o Might not converge but likely to, fast • Newton-Raphson method o Uses derivative of function o Fast convergence (not guaranteed) o Derivation might be analytical (exact) or numerically extimated Numerical Integration • Midpoint method – error O(h 2 ) • Trapezoidal method – error O(h 2 ) • Simpson’s method – error O(h 5 ) • Monte Carlo methods Initial Value Problems (ODE’s) • Euler’s method for growing function • Runge-Kutta method • Applications in two variables...
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algorithm%20topics - • Secant method o Two initial...

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