- Get Best Price Guarantee + 30% Extra Discount

- support@crazyforstudy.com
- +1 (775) 500-0051

- 797 step-by-step solutions
- Solved by professors & experts
- iOS, Android, & web

- Question : P l . 1 . 1 - Suppose A E Rn x n and x E Rr arc given. Give an algorithm for computing the first column of M = (A - :r.11}
- Question : P l . 1 . 2 - In a conventional 2-by-2 matrix multiplication C = AB, there are eight multiplications: a11 bu, aub12, a21bu, a21b12, ai2b21, a12??2. a22b21, and a22b22. Make a table that indicates the order that these multiplications are performed for the ijk, jik, kij , ikj , jki, and kji matrix multiplication algorithms
- Question : P l . 1 . 3 - Give an O(n2) algorithm for computing C = (xyT)k where x and y are n-vectors
- Question : P l . 1 . 4 - Suppose D = ABC where A E Rm x n, B E wxv, and C E wx q. Compare the flop count of an algorithm that computes D via the formula D = (AB)C versus the flop count for an algorithm that computes D using D = A(BC) . Under what conditions is the former procedure more flop-efficient than the latter
- Question : P l . 1 . 5 - Suppose we have real n-by-n matrices C, D, E, and F. Show how to compute real n-by-n matrices A and B with just three real n-by-n matrix multiplications so that A + iB = (C + iD)(E + i F).
- Question : P l . 1 . 6 - Suppose W E Rnxn is defined by n n Wij L L Xip Ypq Zqj p=l q = l Chapter 1. Matrix Multiplication where X, Y, Z E Rnxn. If we use this formula for each Wij then it would require O(n4 ) operations to set up W. On the other hand, = tXip (tYpq Zqj ) = p=l q=l where U = YZ. Thus, W = XU = XYZ and only O(n3 ) operations are required. by Use this methodology to develop an O(n3 ) procedure for computing the n-by-n matrix A defined n n n Q;j = L L L E(k1 , i)F(k1 , i)G(k2 , k1 )H(k2 , k3 )F(k2 , k3 )G(k3 , j) k1 = l k2 = 1 k3 = 1 where E, F, G, H E Rnxn. Hint. Transposes and pointwise products are involved. Notes
- Question : Pl.2.1 - Give an algorithm that overwrites A with A2 where A E Ir x n. How much extra storage is required? Repeat for the case when A is upper triangular
- Question : Pl.2.2 - Specify an algorithm that computes the first column of the matrix M = (A - >.1 !)
- Question : Pl.2.3 - Give a column saxpy algorithm for the n-by-n matrix multiplication problem C = C + AB where A is upper triangular and B is lower triangular.
- Question : Pl.2.4 - Extend Algorithm 1 .2.2 so that it can handle rectangular band matrices. Be sure to describe the underlying data structure
- Question : Pl.2.5 - If A = B + iC is Hermitian with B E R'' x n, then it is easy to show that BT = B and er = -C. Suppose we represent A in an array A . herm with the property that A.herm(i, j) houses b;j if i ::=:: j and Cij if j > i. Using this data structure, write a matrix-vector multiply function that computes Re(z) and lm(z) from Re(x) and lm (x) so that z = Ax.
- Question : Pl.2.6 - Suppose X E R'' x p and A E R'' x n arc given and that A is symmetric. Give an algorithm for computing B = xr AX assuming that both A and B are to be stored using the symmetric storage scheme presented in
- Question : Pl.2.7 - Suppose a E Rn is given and that A E Rn x n has the property that a;j = ali-il+l
- Question : Pl.2.8 - Suppose a E Rn is given and that A E Rn x n has the property that a;j = a((i+j-l) mod n)+l
- Question : Pl.2.9 - Develop a compact storage scheme for symmetric band matrices and write the corresponding gaxpy algorithm
- Question : Pl.2.10 - Suppose A E Rn x n, u E Rn , and v E Rn are given and that k ?? n is an integer. Show how to compute X E R'' x k and Y E R'' x k so that (A + uvT )k = Ak + XYT . How many flops are required? P l
- Question : Pl.2.11 - Suppose x E Rn . Write a single-loop algorithm that computes y = V??x where k is a positive integer and 'Dn is defined in
- Question : Pl.2.12 - (a) Verify ( 1 .2.4) . (b) Show that P'I,r = 'Pr,p
- Question : Pl.2.13 - The number of n-by-n permutation matrices is n ! . How many of these are symmetric?
- Question : P l . 3 . 1 - Rigorously prove the following block matrix equation
- Question : P l . 3 . 2 - Suppose M E Rnxn is Hamiltonian. How many flops are required to compute N = M2?
- Question : P l . 3 . 3 - What can you say about the 2-by-2 block structure of a matrix A E R2nx2n that satisfies
- Question : P l . 3 . 4 - Suppose A = [ :T ?? ] where B E Rnxn is upper bidiagonal. Describe the structure of T = PAPT where P = P2.n is the perfect shuffle permutation defined in
- Question : P l . 3 . 5 - Show that i f B and C are each permutation matrices, then B 18> C i s also a permutation matrix.
- Question : P l . 3 . 6 - Verify Equation ( 1 .3.5
- Question : P l . 3 . 7 - Verify that if x E R"' and y E Rn, then y 18> x = vec (xyT) .
- Question : P l . 3 . 8 - Show that i f B E Jl!'x P, C E Rqxq, and then x [ :: l xT ( B
- Question : P l . 3 . 9 - Suppose A(k) E Rnk xni. for k = l:r and that x E Rn where n = n1
- Question : P l . 3 . 10 - Suppose n is even and define the following function from Rn to R: n/2 f(x) = x ( 1 :2:n)T x(2:2:n) = L x2;-1x2; . i= l (a) Show that if x, y E Rn then n/2 xT y = L:(x2;-1 + Y2;)(x2; + Y2i-J ) - f(x) - f(y). i= l (b) Now consider the n-by-n matrix multiplication C = AB. Give an algorithm for computing this product that requires n3 /2 multiplies once f is applied to the rows of A and the columns of B. See Winograd ( 1 968) for details
- Question : P l . 3 . 1 2 - Adapt strass so that it can handle square matrix multiplication of any order. Hint: If the "current" A has odd dimension, append a zero row and column.
- Question : P l . 3 . 1 3 - Adapt strass so that it can handle nonsquare products, e.g. , C = AB where A E Rmx
- Question : P l . 3 . 1 4 - Let Wn be the number of flops that strass requires to compute an n-by-n product where n is a power of 2. Note that W2 = 25 and that for n 2: 4 Wn = 7Wn/2 + 18(n/2)2
- Question : P l . 3 . 1 5 - Suppose B E Rm 1 x n i , C E irn2 x n2 , and D E Rma x na. Show how to compute the vector y = (B
- Question : Pl.4.1 - Suppose w = [ 1, Wn, wa, . . . ' w??/2-1 ] where n = 2t. Using the colon notation, express [ 2 r/2-1 ] 1 , Wr
- Question : Pl.4.2 - Suppose n = 3m and examine G = [ Fn(:, 1 :3:n - 1 ) I Fn(:, 2:3:n - 1 ) I Fn(:, 3:3:n - 1) ] as a 3-by-3 block matrix, looking for scaled copies of Fm. Based on what you find, develop a recursive radix-3 FFT analogous to the radix-2 implementation in the text.
- Question : Pl.4.3 - If n = 2t, then it can be shown that Fn = (AtI't)
- Question : Pl.4.4 - What fraction of the components of Wn are zero?
- Question : Pl.4.5 - Using (1 .4.13), verify by induction that if n = 2t, then the Haar tranform matrix Wn has the factorization Wn = Ht
- Question : Pl.4.6 - Using ( 1 . 4 . 1 3 ) , develop an O(n) procedure for solving Wn Y = x where x E R" is given and n = 2t .
- Question : P l . 5 . 1 - Suppose A E R"' x n i s tridiagonal and that the elements along its subdiagonal, diagonal, and superdiagonal are stored in vectors e ( l :n - 1 ) , d( l :n) , and /(2 :n) . Give a vectorized implementation of the n-by-n gaxpy y = y + Ax. Hint: Make use of the vector multiplication operation.
- Question : P l . 5 . 2 - Give an algorithm for computing C = C + AT BA where A and B are n-by-n and B is symmetric. Innermost loops should oversee unit-stride vector operations
- Question : P l . 5 . 3 - Suppose A E wx n is stored in column-major order and that m = m1 M and n = n1 N. Regard A as an M-by-N block matrix with m 1 -by-n1 blocks. Give an algorithm for storing A in a vector A . block ( l :mn) with the property that each block Aij is stored contiguously in column-major order.

The best part? As a CrazyForStudy subscriber, you can view available interactive solutions manuals for each of your classes for one low monthly price. Why buy extra books when you can get all the homework help you need in one place?

Just **$7.00/month**

Get immediate access to 24/7 Homework Help, step-by-step solutions, instant homework answer to over 40 million Textbook solution and Q/A

Pay $7.00/month for Better Grades

4out of 5Gyeongseo JeongMatrix Computations (Johns Hopkins Studies in the Mathematical Sciences) Solutions Manual is an exceptional book where all textbook solutions are in one book. It is very helpful. Thank you so much crazy for study for your amazing services.

5out of 5Amirah WahidahI have taken their services earlier for textbook solutions which helped me to score well. I would prefer their Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) Solutions Manual For excellent scoring in my academic year.

4out of 5William JamesI gotta say that when I got started with Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) I didn't think I was going to learn a lot. Contrary to all of my beliefs, I actually think I learned a great deal about conducting businesses and gaining the ability to understand various aspects of it.

5out of 5Airton Piu Mattozo FilhoMatrix Computations (Johns Hopkins Studies in the Mathematical Sciences) Solutions Manual is an exceptional book where all textbook solutions are in one book. It is very helpful. Thank you so much crazy for study for your amazing services.

5out of 5CarlosI have taken their services earlier for textbook solutions which helped me to score well. I would prefer their Matrix Computations (Johns Hopkins Studies in the Mathematical Sciences) Solutions Manual For excellent scoring in my academic year.