point alg ti+1 approx the following must hold for the algorithm to converge quadratically? Select all that apply. The function f (x) must cross the horizontal axis. g' (x*) = 0 The initial iterate is close to *. The fixed point algorithm is only linearly convergent.
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A: The complete C code is given below with output screenshot
Please do not give solution in image format thanku
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- Given a sequence X[1, . . . , n], find an increasing subsequence with the maximum sum. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.Given a sequence X[1, . . . , n], find a longest increasing subsequence. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.Let x0 = (2, 1). Following the general optimization algorithm find solution x2 if for iteration #1 step size α0 = 2 and search direction p0 = (0, 1), and for iteration #2 α1 = 3 and p1 = (2, 0). Show solutions x0, x1, x2 using cartesian coordinates
- Apply a suitable approach to compare the asymptotic order of growth forthe following pair of functions. Prove your answer and conclude by telling if f(n) ?Ѳ(g(n)), f(n) ?O(g(n)) or f(n) ?Ω(g(n)). f(n) = 100n2+ 20 AND g(n) = n + log nQ2:Identify if the following statement is true or false, explain your reasoning. For any NP-Optimization problem there exist polynomial-time approximation algorithms for that problem that have worst-case approximation ratios arbitrarily close to 1.Given an array of intervals I[1, . . . , n] where I[i] = [si, fi], find the minimumnumber of intervals you need to remove to make the rest of the intervals non-overlapping. Precisely define the subproblem.Provide the recurrence equation.Describe the algorithm in pseudocode to compute the optimal value.Describe the algorithm in pseudocode to print out an optimal solution.
- Consider the SeldeLP algorithm. Create a scenario to illustrate how the linear program's optimum as defined by B(Hh) u h may vary from the linear program's optimum as defined by H.How would you modify the dynamic programming algorithm for the coin collecting problem if some cells on the board are inaccessible for the robot? Apply your algorithm to the board below, where the inaccessible cells are shown by X’s. How many optimal paths are there for this board? You need to provide 1) a modified recurrence relation, 2) a pseudo code description of the algorithm, and 3) a table that stores solutions to the subproblems.Match the following sentence to the best suitable answer: - A. B. C. D. for the linear congruence ax=1(mod m), x is the inverse of a, if__________ - A. B. C. D. What is -4 mod 9 ? - A. B. C. D. The solution exists for a congruence ax=b(mod m) such that GCD(a,m)=1 and - A. B. C. D. (107+22)mod 10 is equivalent to :_________ A. 5 B. c divides b C. GCD(a,m)=1 D. 9 mod 10
- The branching part of the branch and bound algorithm that Solver uses to solve integer optimization models means that the algorithm [a] creates subsets of solutions through which to search[b] searches through only a limited set of feasible integer solutions [c] identifies an incumbent solution which is optimal [d] uses a decision tree to find the optimal solution 2. The LP relaxation of an integer programming (IP) problem is typically easy to solve and provides a bound for the IP model. [a] True [b] False(a) Which Gradient Descent algorithm (stochastic, batch, mini batch)will reach the vicinity of the optimal solution the fastest? (b) Which will actually converge?(c) How can you make the others converge as well? Explain.In this problem we have n jobs j1, j2, ..., jn, each has an associated deadline d1, d2, ..., dn and profit p1, p2, ..., pn. Profit will only be awarded or earned if the job is completed before the deadline. We assume that each job takes 1 unit of time to complete. The objective is to earn maximum profit when only one job can be scheduled or processed at any given time.Provide the pseudocode of an algorithm to find the sequence of jobs to do with the maximum total profit. Also describe the main idea of your algorithm using plain language.[Hint: You can select the jobs in a greedy way. You can use the following example to help your analysis.] Job J1 J2 J3 J4 J5 Deadline 2 1 3 2 1 Profit 60 100 20 40 20 The best job sequence would be J2 →J1 →J3.