The Collaborative International Dictionary of English v.0.48:

Rigorous \Rig"or*ous\, a. [F. rigoureux, LL. rigorosus. See
   Rigor.]
   1. Manifesting, exercising, or favoring rigor; allowing no
      abatement or mitigation; scrupulously accurate; exact;
      strict; severe; relentless; as, a rigorous officer of
      justice; a rigorous execution of law; a rigorous
      definition or demonstration.
      [1913 Webster]

            He shall be thrown down the Tarpeian Rock
            With rigorous hands.                  --Shak.
      [1913 Webster]

            We do not connect the scattered phenomena into their
            rigorous unity.                       --De Quincey.
      [1913 Webster]

   2. Severe; intense; inclement; as, a rigorous winter.
      [1913 Webster]

   3. Violent. [Obs.] "Rigorous uproar." --Spenser.
      [1913 Webster]

   4. (Mathematics, Logic) Adhering scrupulously and exactly to
      accepted principles; hence, logically valid; as, a
      rigorous proof.
      [PJC]

   Syn: Rigid; inflexible; unyielding; stiff; severe; austere;
        stern; harsh; strict; exact.
        [1913 Webster] -- Rig"or*ous*ly, adv. --
        Rig"or*ous*ness, n.
        [1913 Webster]

WordNet (r) 3.0 (2006):

rigorousness
    n 1: something hard to endure; "the asperity of northern
         winters" [syn: asperity, grimness, hardship, rigor,
         rigour, severity, severeness, rigorousness,
         rigourousness]
    2: excessive sternness; "severity of character"; "the harshness
       of his punishment was inhuman"; "the rigors of boot camp"
       [syn: severity, severeness, harshness, rigor,
       rigour, rigorousness, rigourousness, inclemency,
       hardness, stiffness]