By Joe Pitt-Francis, Jonathan Whiteley
This easy-to-read textbook/reference offers a necessary advisor to object-oriented C++ programming for clinical computing. With a pragmatic concentrate on studying by way of instance, the idea is supported through various workouts. positive aspects: presents a selected specialise in the appliance of C++ to clinical computing, together with parallel computing utilizing MPI; stresses the significance of a transparent programming kind to lessen the advent of mistakes into code; provides a realistic creation to procedural programming in C++, masking variables, circulate of keep watch over, enter and output, tips, capabilities, and reference variables; indicates the efficacy of periods, highlighting the most positive aspects of object-orientation; examines extra complicated C++ gains, resembling templates and exceptions; provides valuable suggestions and examples in the course of the textual content, including chapter-ending routines, and code to be had to obtain from Springer.
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This algorithm may be terminated when |xi − xi−1 | < ε for some user-prescribed ε. In this exercise, we will apply the Newton–Raphson algorithm to the function f (x) = ex + x 3 − 5, with initial guess x0 = 0. 1. Write down (on paper) the Newton–Raphson iteration for this choice of f (x). 2. By using a for loop, and an array for the iterates xi , write a program that implements the Newton–Raphson iteration for i = 1, 2, 3, . . , 100. Print out the value of xi on each iteration, and confirm that the iteration does converge as i increases.
2 for a definition of the scalar product, and Sect. 4 Write code that declares four 2 × 2 matrices of double precision floating point numbers, A, B, C, D, and assigns values to the entries of A and B. Let C = A + B, and D=AB. Extend your code so that it calculates the entries of C and D, and then prints the entries of these matrices to screen. 5 Write code that invites the user to input separately strings that store their given name and their family name. Print the user’s full name to screen. 6 I want to record the number of cars that drive past my house each day for five consecutive days, and calculate the average of these numbers.
3. Think of a check that can be performed on the iterates xi , as i becomes larger, that allows you to have confidence that your solution is correct. Implement this check in your program. 4. It is not necessary to store the value of xi on each iteration to implement the Newton–Raphson algorithm. All that is needed is the previous iterate, xi−1 , and the current iterate, xi . Modify your code so that the array representing xi , i = 1, 2, . . , 100 is replaced by two scalar variables, x_prev and x_next.