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Lecture Notes for CMSC 878R - ADV TOP NUM METH at Maryland (UMD)
Assignment Information
| Material Type: | Assignment 2 |
| Professor: | Staff |
| Class: | CMSC 878R - ADV TOP NUM METH |
| Subject: | Computer Science |
| University: | University of Maryland |
| Term: | -- |
Sample Document Text
Problem (Homework 2)
This week's assignment uses the ideas of using Taylor series to achieve factorizations
suitable for use in FMM type algorithms. Using this tool to develop a factorization, we will
develop a new version of the fast Gauss transform (FGT).
Let
?
ji
= e
?(y
j
?x
i
)
2
, i = 1,...,N, j = 1,...,M.
? =
?
11
?
12
... ?
1N
?
21
?
22
... ?
2N
... ... ... ...
?
M1
?
M2
... ?
MN
, u =
u
1
u
2
u
3
...
u
N
, v =
v
1
v
2
v
3
...
v
M
, #
where x
1
,...,x
N
, y
1
,...,y
M
,u
1
,...,u
N
, are random numbers distributed uniformly in [0,1] .
Compute the matrix-vector product
v = ?u, #
or
v
j
=
?
i=1
N
?
ji
u
i
, j = 1,...,M, #
with absolute error ? < 10
?6
. The matrix sizes, N,M > 0 are given (fixed) positive integers.
1. Using the example from Lecture #2, write down a factored expression. Estimate the error
in truncating the series using residual term evaluation for the Taylor series, and evaluate
the tru...
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