Question: Background. Recall from Lecture 15 that the linear least square (LLS) problem Ax= b can be re-written as Rx = QTb, ( * ) using

Background. Recall from Lecture 15 that the linear least square (LLS) problem Ax"=" b can be re-written as Rx = QTb, ( * ) using the thin QR factorization A = QR. Multiplying (*) by R-1 gives a formula for the pseudoinverse At = R-QT. (* * ) The whole process can be turned into the following QR-based algorithm for LLS problem: 1. Factor A = QR. 2. Let z = QTb. 3. Solve Rx = z for x using backward substitution. Questions. Now assuming A is a real matrix, establish analogous results using the thin SVD, A = DEVT. (@) That is: (a) (9 points) Derive an equation similar to (.) by substituting (O) into the associated normal equation. (b) (9 points) Find an alternate formula for At using the result of part (a). (c) (12 points) Write down an SVD-based algorithm for LLS problem using the result of part (a)

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