Something like this;

public static IList<double> Parse(string text)
{
    List<double> list = new List<double>();
    if (text != null)
    {
        StringBuilder dbl = new StringBuilder(30); 
        for (int i = 0; i < text.Length; i++)
        {
            if (text[i] == 'm')
            {
                list.Add(double.Parse(dbl.ToString(), CultureInfo.InvariantCulture));
                dbl.Length = 0;
            }
            else
            {
                if ((text[i] != ' ') && (text[i] != '/'))
                {
                    dbl.Append(text[i]);
                }
            }
        }
    }
    return list;
}

It does not use Regex, allocates only the needed array, and a fixed size StringBuilder. And if the text was provided as a TextReader instead of a string, you could change the returned IList into an IEnumerable, use yield instead of Add, and optimize memory consumption.