MATH 405 Midterm: MATH 405+607E 2016 Winter Test 1
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Instructions: you have 150 minutes to write this exam, this exam contains 5 pages including this cover page. If you require more space, label clearly where you have written your solution: no aids are allowed. Simple calculators are acceptable, but should not be needed. A singular matrix has a zero condition number. A composite quadrature method is a method that adaptively chooses the best grid to approximate an integral. The barycentric lagrange formula is one possible technique for eval- uating an interpolating polynomial. Radial basis function methods approximate a function u(~x) as a i wi (||~x ~xi||2). weighted sum of radial functions: u(~x) =pn. Even if the grid points x0, x1, . , xn are not distinct, the interpo- lating polynomial of degree n is still unique. Label your diagram. (h) give the cardinal polynomial ln,k(x) The following matrix problems approximate the di erential equation uxx = f .
