MATH 128b Numerical Analysis Berkeley

1 Math128B Mar. 21, 2005 Jonathan Dorfman Homework 8 Solutions Problem 8.1 & 8.2 le Hmwk8Main.m function calls NLShooting to solve BVP: y (t) = y 2 y + log x, x [1, 2], y(1) = 0, y(2) = log 2 calls NLFiniteDi to solve BVP: y (t) = y 2 y + log x,

1 Math128B Feb. 19, 2005 Jonathan Dorfman Homework 5 Solutions le Hmwk5Main.m Householder.m QRShift.m function cooks up random matrix A, symmetrizes it to B, and also predened 3x3 symmetric C calls Householder on B to reduce to symmetric tridiago

1 Math128B May. 6, 2005 Jonathan Dorfman Homework 11 Solutions le Hmwk11Main.m CreateBkN.m Lagrange.m FormatPoly.m SchoenbergWhitney.m Bezier.m Binomial.m function calls CreateBkN, Langrange, FormatPoly calls SchoenbergWhitney calls Bezier create

1 Math128B Mar. 1, 2005 Jonathan Dorfman Homework 6 Solutions le Hmwk6Main.m function calls Euler (Problem 1) to compute v(6) for IVP: v (t) = 32 0.032 v 2 , v(0) = 0 calls Heun (Problem 2) to solve IVP: y (t) = t2 y, t [0, 2], y(0) = 1 calls T

1 Math128B Mar. 12, 2005 Jonathan Dorfman Homework 7 Solutions le Hmwk7Main.m RungeKutta4.m Shooting.m FiniteDi.m DF7 1.m DF7 2 homog.m DF7 2 inhom.m cosmetics.m function calls RungeKutta4 to solve IVP: 2x 5x 3x = 45e2t , x(0) = 2, x (0) = 1, t

1 Math128B January 28, 2005 Jonathan Dorfman Background Material on Norms denotes the p-norm of a vector in Rn . If no p is indicated, then p = 2 is assumed. 1. x p 2. We dene the operator p-norm of A as A def p = sup x=0 A x p p = sup x p =1

1 Math128B Feb. 6, 2005 Jonathan Dorfman Homework 3 Solutions (#1-#4) le Hmwk3Main.m PowerMethod.m JacobiMethod.m GaussSeidel.m SORMethod.m DisplayPerf.m function receives matrix A, row vector x0, tolerance tol, and row vector b as input implements

1 Math128B Feb. 1, 2005 Jonathan Dorfman Homework 2 Solutions Problem 2.1 First, a quick review of some facts about complex numbers: 1. for z = x + iy = r cos + ir sin = rei C we have (magnitude of complex scalar) |z| = def x2 + y 2 = r 2. if

Homework #10 Math 128B - Spring 2003 DUE 04/22/03 (60 points) Each problem is worth 5 points unless otherwise specied. 1) Section 11.1: # 1, 6, 8, 9, 10. 2) Section 11.2: # 3(b). 3) Section 11.3: # 1, 5, (10 points) 7. 4) Section 11.4: # (10 points)