MATH 307 Lecture Notes - Lecture 4: Operator Norm, Alt-J, Numerical Stability
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Recall thedef ofnorms e x 11 111,11 11x. Itall max hax g o lbydef of 11amop. Generally computing 11all for a general matrix a may not be easy but simplefor a diagonal matrix. Suppose we use to norm for vectors l. E j13112 t 13 212 t 13 312. 1117 112 e3 forany non zero vector x for an x. When wesolve a system of linear equation ax b the solution is numerically stable the vector b is often measurements. So b is subject to error changes drastically even for slight error in b sayob observations or we want. Finite computer memory cannot store most of real sexactly. Q what kind of solution say i we couldget if wesolve ax b with b t ob instead of b i e ai bt ob i. Let ob i oo o to b fwmi.
