Lecture08-nonhomogeneous

# Lecture08-nonhomogeneous - are exactly n roots Â They may...

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CS 312: Algorithm Analysis Lecture #8: Non- Homogeneous Recurrence Relations This work is licensed under a Creative Commons Attribution-Share Alike 3.0 Unported License. Slides by: Eric Ringger, with contributions from Mike Jones, Eric Mercer, Sean Warnick

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Announcements § HW #5 Due Today § Questions about Homogeneous RR? § Project #2 § Questions about the project? § Early Day: Friday § Due Date: next Monday
Objectives § Define “roots of multiplicity j” § Understand how to solve non-homogeneous , linear, recurrence relations with constant coefficients § Geometric forcing function § Find the specific solution from initial conditions

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Example (cont.): Linear, Homogeneous Recurrence Relation

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Finding the Particular Solution
Finding the Particular Solution

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Fibonacci in Closed Form!
Fibonacci in Closed Form!

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Fundamental Theorem of Algebra § For every polynomial of degree n, there

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Unformatted text preview: are exactly n roots. Â§ They may not be unique. Roots of Multiplicity j Roots of Multiplicity j Roots of Multiplicity j Roots of Multiplicity j Roots of Multiplicity j Example Example Non-Homogeneous, Linear Recurrence Relations Non-Homogeneous Example What do you notice about the problem now? Non-Homogeneous Example What do you notice about the problem now? Example (Cont.): d=0 Example (Cont.): d=0 Possible Update Â§ Point out existence of homog. RR for every non-homog. RR. Â§ Notation: Use y(k) (homog.) instead of z(k) (non-homog.) to emphasize the difference. Initial Conditions Initial Conditions Example (cont.) Example (cont.) Towers of Hanoi Revisited Towers of Hanoi Revisited Assignment Â§ Read: Recurrence Relations Notes, Parts III & IV Â§ HW #6: Part II Exercises (Section 2.2)...
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