Download e-book for iPad: An Introduction to Parallel and Vector Scientific Computing by Ronald W. Shonkwiler
By Ronald W. Shonkwiler
During this textual content, scholars of utilized arithmetic, technology and engineering are brought to basic methods of pondering the wide context of parallelism. The authors start through giving the reader a deeper knowing of the problems via a common exam of timing, information dependencies, and verbal exchange. those principles are carried out with recognize to shared reminiscence, parallel and vector processing, and allotted reminiscence cluster computing. Threads, OpenMP, and MPI are coated, besides code examples in Fortran, C, and Java. the rules of parallel computation are utilized all through because the authors disguise conventional themes in a primary path in clinical computing. construction at the basics of floating element illustration and numerical errors, an intensive therapy of numerical linear algebra and eigenvector/eigenvalue difficulties is equipped. through learning how those algorithms parallelize, the reader is ready to discover parallelism inherent in different computations, reminiscent of Monte Carlo equipment.
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Now perform the following steps: a. b. c. d. e. compute x 2 , . . , x r ; compute q1 (x), . . , qs (x); compute x r , x 2r , . . , x (s−1)r ; multiply x r q2 (x), x 2r q3 (x),. . , x (s−1)r qs (x); add a0 + q1 (x) + x r q2 (x) + · · · + x (s−1)r qs (x). 13. (5) Let A be an n × n upper triangular matrix such that aii = 0 for 1 ≤ i ≤ n, and let b be an n-dimensional vector. The Back Substitution method to solve the linear system Ax = b begins with determining xn by solving the scalar equation ann xn = bn .
10,000, namely yi = xi ∗ xi + xi ∗ xi ∗ xi yi = xi ∗ (xi + xi ∗ xi ) yi = xi ∗ xi ∗ (1 + xi ). 6. 7. 8. 9. Calculate the time for each using the Vector Timing Data Table (p. 11). Be sure to take chaining (saxpy operations) into consideration. (2) Using the Vector Timing Data Table (p. 11), what is the MFLOP rate for a vector add operation as a function of vector length N ? (3) The matrix–vector product y = Ax, where A is upper triangular, ai j = 0, j < i, i = 1, . . , n, and x is the vector of 1s, is to be done on a vector computer.
4. (3) The speed of an electronic signal in a wire is about 2/3 the speed of light in a vacuum (186,000 miles/s or 299,792,458 m/s). 4 gHz, how far does an electronic signal travel in one clock cycle? How far for a bus speed of 266 mHz? 5. (4) Consider three ways of computing xi2 + xi3 , i = 1, . . , 10,000, namely yi = xi ∗ xi + xi ∗ xi ∗ xi yi = xi ∗ (xi + xi ∗ xi ) yi = xi ∗ xi ∗ (1 + xi ). 6. 7. 8. 9. Calculate the time for each using the Vector Timing Data Table (p. 11). Be sure to take chaining (saxpy operations) into consideration.